LMFDB - Embedded newform 260.2.p.d.207.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(103,260)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("260.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.p (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			207.12
Character	$\chi$	$=$	260.207
Dual form			260.2.p.d.103.12

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.601658 - 1.27985i) q^{2} +(-1.55255 - 1.55255i) q^{3} +(-1.27602 + 1.54006i) q^{4} +(-1.95736 + 1.08109i) q^{5} +(-1.05293 + 2.92114i) q^{6} +(3.02953 + 3.02953i) q^{7} +(2.73876 + 0.706517i) q^{8} +1.82084i q^{9} +O(q^{10})$	\(q+(-0.601658 - 1.27985i) q^{2} +(-1.55255 - 1.55255i) q^{3} +(-1.27602 + 1.54006i) q^{4} +(-1.95736 + 1.08109i) q^{5} +(-1.05293 + 2.92114i) q^{6} +(3.02953 + 3.02953i) q^{7} +(2.73876 + 0.706517i) q^{8} +1.82084i q^{9} +(2.56129 + 1.85467i) q^{10} -4.00418 q^{11} +(4.37211 - 0.409941i) q^{12} +(3.48257 + 0.933659i) q^{13} +(2.05459 - 5.70007i) q^{14} +(4.71735 + 1.36045i) q^{15} +(-0.743565 - 3.93028i) q^{16} +(-0.753955 - 0.753955i) q^{17} +(2.33040 - 1.09552i) q^{18} +4.01929i q^{19} +(0.832676 - 4.39393i) q^{20} -9.40700i q^{21} +(2.40915 + 5.12474i) q^{22} +(3.75800 + 3.75800i) q^{23} +(-3.15517 - 5.34898i) q^{24} +(2.66249 - 4.23216i) q^{25} +(-0.900372 - 5.01890i) q^{26} +(-1.83070 + 1.83070i) q^{27} +(-8.53137 + 0.799924i) q^{28} +6.60247i q^{29} +(-1.09706 - 6.85601i) q^{30} +2.35636 q^{31} +(-4.58279 + 3.31633i) q^{32} +(6.21670 + 6.21670i) q^{33} +(-0.511324 + 1.41857i) q^{34} +(-9.20505 - 2.65467i) q^{35} +(-2.80421 - 2.32343i) q^{36} +(0.454487 - 0.454487i) q^{37} +(5.14408 - 2.41824i) q^{38} +(-3.95732 - 6.85643i) q^{39} +(-6.12455 + 1.57795i) q^{40} +5.01258i q^{41} +(-12.0395 + 5.65979i) q^{42} +(4.32686 + 4.32686i) q^{43} +(5.10940 - 6.16667i) q^{44} +(-1.96850 - 3.56404i) q^{45} +(2.54863 - 7.07069i) q^{46} +(3.87211 + 3.87211i) q^{47} +(-4.94755 + 7.25639i) q^{48} +11.3561i q^{49} +(-7.01842 - 0.861267i) q^{50} +2.34111i q^{51} +(-5.88170 + 4.17200i) q^{52} +(1.34709 - 1.34709i) q^{53} +(3.44448 + 1.24156i) q^{54} +(7.83761 - 4.32888i) q^{55} +(6.15675 + 10.4376i) q^{56} +(6.24016 - 6.24016i) q^{57} +(8.45015 - 3.97243i) q^{58} -0.838004i q^{59} +(-8.11459 + 5.52904i) q^{60} -13.3586 q^{61} +(-1.41772 - 3.01578i) q^{62} +(-5.51629 + 5.51629i) q^{63} +(7.00167 + 3.86997i) q^{64} +(-7.82600 + 1.93747i) q^{65} +(4.21610 - 11.6968i) q^{66} +(-3.69649 - 3.69649i) q^{67} +(2.12319 - 0.199076i) q^{68} -11.6690i q^{69} +(2.14072 + 13.3783i) q^{70} -14.6839 q^{71} +(-1.28646 + 4.98686i) q^{72} +(-5.33956 - 5.33956i) q^{73} +(-0.855119 - 0.308228i) q^{74} +(-10.7043 + 2.43700i) q^{75} +(-6.18994 - 5.12868i) q^{76} +(-12.1308 - 12.1308i) q^{77} +(-6.39423 + 9.18998i) q^{78} +3.43974 q^{79} +(5.70441 + 6.88910i) q^{80} +11.1471 q^{81} +(6.41534 - 3.01586i) q^{82} +(4.47418 - 4.47418i) q^{83} +(14.4873 + 12.0035i) q^{84} +(2.29085 + 0.660665i) q^{85} +(2.93443 - 8.14100i) q^{86} +(10.2507 - 10.2507i) q^{87} +(-10.9665 - 2.82902i) q^{88} -6.30698 q^{89} +(-3.37706 + 4.66371i) q^{90} +(7.72198 + 13.3791i) q^{91} +(-10.5828 + 0.992272i) q^{92} +(-3.65837 - 3.65837i) q^{93} +(2.62602 - 7.28539i) q^{94} +(-4.34522 - 7.86718i) q^{95} +(12.2638 + 1.96624i) q^{96} +(-9.64616 + 9.64616i) q^{97} +(14.5340 - 6.83245i) q^{98} -7.29099i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q+O(q^{10}) $ 64 * q	$ 64 q - 24 q^{12} - 4 q^{16} - 40 q^{17} - 36 q^{22} + 44 q^{26} + 24 q^{30} + 28 q^{36} + 16 q^{38} - 44 q^{40} + 8 q^{42} - 44 q^{48} + 56 q^{52} - 48 q^{53} - 64 q^{56} + 80 q^{61} + 20 q^{62} - 72 q^{65} - 24 q^{66} - 76 q^{68} - 112 q^{77} - 20 q^{78} + 80 q^{81} + 52 q^{82} - 152 q^{88} - 64 q^{90} + 56 q^{92}+O(q^{100}) $ 64 * q - 24 * q^12 - 4 * q^16 - 40 * q^17 - 36 * q^22 + 44 * q^26 + 24 * q^30 + 28 * q^36 + 16 * q^38 - 44 * q^40 + 8 * q^42 - 44 * q^48 + 56 * q^52 - 48 * q^53 - 64 * q^56 + 80 * q^61 + 20 * q^62 - 72 * q^65 - 24 * q^66 - 76 * q^68 - 112 * q^77 - 20 * q^78 + 80 * q^81 + 52 * q^82 - 152 * q^88 - 64 * q^90 + 56 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.601658	−	1.27985i	−0.425436	−	0.904988i
$2$	−0.601658	−	1.27985i	−0.425436	−	0.904988i
$3$	−1.55255	−	1.55255i	−0.896367	−	0.896367i	0.0987456	−	0.995113i	$-0.468517\pi$
$3$	−1.55255	−	1.55255i	−0.896367	−	0.896367i	−0.995113	+	0.0987456i	$0.968517\pi$
$4$	−1.27602	+	1.54006i	−0.638008	+	0.770030i
$5$	−1.95736	+	1.08109i	−0.875356	+	0.483478i
$5$	−1.95736	+	1.08109i	−0.875356	+	0.483478i
$6$	−1.05293	+	2.92114i	−0.429855	+	1.19255i
$7$	3.02953	+	3.02953i	1.14505	+	1.14505i	0.987513	+	0.157541i	$0.0503565\pi$
$7$	3.02953	+	3.02953i	1.14505	+	1.14505i	0.157541	+	0.987513i	$0.449643\pi$
$8$	2.73876	+	0.706517i	0.968300	+	0.249792i
$9$			1.82084i			0.606948i
$10$	2.56129	+	1.85467i	0.809950	+	0.586498i
$11$	−4.00418			−1.20731			−0.603653	−	0.797247i	$-0.706289\pi$
$11$	−4.00418			−1.20731			−0.603653	+	0.797247i	$0.706289\pi$
$12$	4.37211	−	0.409941i	1.26212	−	0.118340i
$13$	3.48257	+	0.933659i	0.965891	+	0.258951i
$13$	3.48257	+	0.933659i	0.965891	+	0.258951i
$14$	2.05459	−	5.70007i	0.549113	−	1.52341i
$15$	4.71735	+	1.36045i	1.21801	+	0.351267i
$16$	−0.743565	−	3.93028i	−0.185891	−	0.982570i
$17$	−0.753955	−	0.753955i	−0.182861	−	0.182861i	0.609740	−	0.792601i	$-0.291274\pi$
$17$	−0.753955	−	0.753955i	−0.182861	−	0.182861i	−0.792601	+	0.609740i	$0.791274\pi$
$18$	2.33040	−	1.09552i	0.549281	−	0.258218i
$19$			4.01929i			0.922088i	0.887377	+	0.461044i	$0.152525\pi$
$19$			4.01929i			0.922088i	−0.887377	+	0.461044i	$0.847475\pi$
$20$	0.832676	−	4.39393i	0.186192	−	0.982513i
$21$		−	9.40700i		−	2.05278i
$22$	2.40915	+	5.12474i	0.513632	+	1.09260i
$23$	3.75800	+	3.75800i	0.783597	+	0.783597i	0.980436	−	0.196839i	$-0.0630676\pi$
$23$	3.75800	+	3.75800i	0.783597	+	0.783597i	−0.196839	+	0.980436i	$0.563068\pi$
$24$	−3.15517	−	5.34898i	−0.644047	−	1.09186i
$25$	2.66249	−	4.23216i	0.532498	−	0.846432i
$26$	−0.900372	−	5.01890i	−0.176578	−	0.984287i
$27$	−1.83070	+	1.83070i	−0.352319	+	0.352319i
$28$	−8.53137	+	0.799924i	−1.61228	+	0.151172i
$29$			6.60247i			1.22605i	0.790064	+	0.613024i	$0.210047\pi$
$29$			6.60247i			1.22605i	−0.790064	+	0.613024i	$0.789953\pi$
$30$	−1.09706	−	6.85601i	−0.200295	−	1.25173i
$31$	2.35636			0.423214			0.211607	−	0.977355i	$-0.432130\pi$
$31$	2.35636			0.423214			0.211607	+	0.977355i	$0.432130\pi$
$32$	−4.58279	+	3.31633i	−0.810130	+	0.586250i
$33$	6.21670	+	6.21670i	1.08219	+	1.08219i
$34$	−0.511324	+	1.41857i	−0.0876914	+	0.243283i
$35$	−9.20505	−	2.65467i	−1.55594	−	0.448721i
$36$	−2.80421	−	2.32343i	−0.467368	−	0.387238i
$37$	0.454487	−	0.454487i	0.0747172	−	0.0747172i	−0.668761	−	0.743478i	$-0.733175\pi$
$37$	0.454487	−	0.454487i	0.0747172	−	0.0747172i	0.743478	+	0.668761i	$0.233175\pi$
$38$	5.14408	−	2.41824i	0.834479	−	0.392290i
$39$	−3.95732	−	6.85643i	−0.633678	−	1.09791i
$40$	−6.12455	+	1.57795i	−0.968376	+	0.249495i
$41$			5.01258i			0.782834i	0.920213	+	0.391417i	$0.128015\pi$
$41$			5.01258i			0.782834i	−0.920213	+	0.391417i	$0.871985\pi$
$42$	−12.0395	+	5.65979i	−1.85774	+	0.873325i
$43$	4.32686	+	4.32686i	0.659840	+	0.659840i	0.955342	−	0.295502i	$-0.0954870\pi$
$43$	4.32686	+	4.32686i	0.659840	+	0.659840i	−0.295502	+	0.955342i	$0.595487\pi$
$44$	5.10940	−	6.16667i	0.770271	−	0.929661i
$45$	−1.96850	−	3.56404i	−0.293446	−	0.531296i
$46$	2.54863	−	7.07069i	0.375776	−	1.04252i
$47$	3.87211	+	3.87211i	0.564805	+	0.564805i	0.930669	−	0.365864i	$-0.119226\pi$
$47$	3.87211	+	3.87211i	0.564805	+	0.564805i	−0.365864	+	0.930669i	$0.619226\pi$
$48$	−4.94755	+	7.25639i	−0.714117	+	1.04737i
$49$			11.3561i			1.62229i
$50$	−7.01842	−	0.861267i	−0.992554	−	0.121802i
$51$			2.34111i			0.327821i
$52$	−5.88170	+	4.17200i	−0.815646	+	0.578552i
$53$	1.34709	−	1.34709i	0.185037	−	0.185037i	−0.608509	−	0.793547i	$-0.708232\pi$
$53$	1.34709	−	1.34709i	0.185037	−	0.185037i	0.793547	+	0.608509i	$0.208232\pi$
$54$	3.44448	+	1.24156i	0.468734	+	0.168955i
$55$	7.83761	−	4.32888i	1.05682	−	0.583706i
$56$	6.15675	+	10.4376i	0.822730	+	1.39478i
$57$	6.24016	−	6.24016i	0.826530	−	0.826530i
$58$	8.45015	−	3.97243i	1.10956	−	0.521605i
$59$		−	0.838004i		−	0.109099i	−0.998511	−	0.0545494i	$-0.982628\pi$
$59$		−	0.838004i		−	0.109099i	0.998511	−	0.0545494i	$-0.0173722\pi$
$60$	−8.11459	+	5.52904i	−1.04759	+	0.713796i
$61$	−13.3586			−1.71039			−0.855194	−	0.518309i	$-0.826562\pi$
$61$	−13.3586			−1.71039			−0.855194	+	0.518309i	$0.826562\pi$
$62$	−1.41772	−	3.01578i	−0.180051	−	0.383004i
$63$	−5.51629	+	5.51629i	−0.694987	+	0.694987i
$64$	7.00167	+	3.86997i	0.875208	+	0.483746i
$65$	−7.82600	+	1.93747i	−0.970695	+	0.240313i
$66$	4.21610	−	11.6968i	0.518966	−	1.43977i
$67$	−3.69649	−	3.69649i	−0.451599	−	0.451599i	0.444286	−	0.895885i	$-0.353457\pi$
$67$	−3.69649	−	3.69649i	−0.451599	−	0.451599i	−0.895885	+	0.444286i	$0.853457\pi$
$68$	2.12319	−	0.199076i	0.257475	−	0.0241416i
$69$		−	11.6690i		−	1.40478i
$70$	2.14072	+	13.3783i	0.255865	+	1.59901i
$71$	−14.6839			−1.74266			−0.871331	−	0.490696i	$-0.836743\pi$
$71$	−14.6839			−1.74266			−0.871331	+	0.490696i	$0.836743\pi$
$72$	−1.28646	+	4.98686i	−0.151610	+	0.587707i
$73$	−5.33956	−	5.33956i	−0.624948	−	0.624948i	0.321844	−	0.946793i	$-0.395697\pi$
$73$	−5.33956	−	5.33956i	−0.624948	−	0.624948i	−0.946793	+	0.321844i	$0.895697\pi$
$74$	−0.855119	−	0.308228i	−0.0994056	−	0.0358308i
$75$	−10.7043	+	2.43700i	−1.23603	+	0.281400i
$76$	−6.18994	−	5.12868i	−0.710035	−	0.588300i
$77$	−12.1308	−	12.1308i	−1.38243	−	1.38243i
$78$	−6.39423	+	9.18998i	−0.724004	+	1.04056i
$79$	3.43974			0.387000			0.193500	−	0.981100i	$-0.438016\pi$
$79$	3.43974			0.387000			0.193500	+	0.981100i	$0.438016\pi$
$80$	5.70441	+	6.88910i	0.637772	+	0.770225i
$81$	11.1471			1.23856
$82$	6.41534	−	3.01586i	0.708455	−	0.333046i
$83$	4.47418	−	4.47418i	0.491105	−	0.491105i	−0.417549	−	0.908654i	$-0.637111\pi$
$83$	4.47418	−	4.47418i	0.491105	−	0.491105i	0.908654	+	0.417549i	$0.137111\pi$
$84$	14.4873	+	12.0035i	1.58070	+	1.30969i
$85$	2.29085	+	0.660665i	0.248478	+	0.0716592i
$86$	2.93443	−	8.14100i	0.316428	−	0.877867i
$87$	10.2507	−	10.2507i	1.09899	−	1.09899i
$88$	−10.9665	−	2.82902i	−1.16903	−	0.301575i
$89$	−6.30698			−0.668539			−0.334269	−	0.942478i	$-0.608489\pi$
$89$	−6.30698			−0.668539			−0.334269	+	0.942478i	$0.608489\pi$
$90$	−3.37706	+	4.66371i	−0.355974	+	0.491598i
$91$	7.72198	+	13.3791i	0.809484	+	1.40251i
$92$	−10.5828	+	0.992272i	−1.10333	+	0.103452i
$93$	−3.65837	−	3.65837i	−0.379355	−	0.379355i
$94$	2.62602	−	7.28539i	0.270854	−	0.751430i
$95$	−4.34522	−	7.86718i	−0.445810	−	0.807156i
$96$	12.2638	+	1.96624i	1.25167	+	0.200678i
$97$	−9.64616	+	9.64616i	−0.979420	+	0.979420i	−0.999792	−	0.0203728i	$-0.993515\pi$
$97$	−9.64616	+	9.64616i	−0.979420	+	0.979420i	0.0203728	+	0.999792i	$0.493515\pi$
$98$	14.5340	−	6.83245i	1.46816	−	0.690182i
$99$		−	7.29099i		−	0.732772i
$100$	3.12040	+	9.50069i	0.312040	+	0.950069i
$101$	10.3409			1.02896			0.514479	−	0.857503i	$-0.327985\pi$
$101$	10.3409			1.02896			0.514479	+	0.857503i	$0.327985\pi$
$102$	2.99626	−	1.40855i	0.296674	−	0.139467i
$103$	3.33400	+	3.33400i	0.328509	+	0.328509i	0.852019	−	0.523511i	$-0.175378\pi$
$103$	3.33400	+	3.33400i	0.328509	+	0.328509i	−0.523511	+	0.852019i	$0.675378\pi$
$104$	8.87829	+	5.01757i	0.870588	+	0.492013i
$105$	10.1698	+	18.4129i	0.992472	+	1.79691i
$106$	−2.53456	−	0.913583i	−0.246178	−	0.0887350i
$107$	7.78916	−	7.78916i	0.753007	−	0.753007i	−0.222033	−	0.975039i	$-0.571269\pi$
$107$	7.78916	−	7.78916i	0.753007	−	0.753007i	0.975039	+	0.222033i	$0.0712691\pi$
$108$	−0.483384	−	5.15540i	−0.0465137	−	0.496078i
$109$	−3.16760			−0.303401			−0.151701	−	0.988426i	$-0.548475\pi$
$109$	−3.16760			−0.303401			−0.151701	+	0.988426i	$0.548475\pi$
$110$	−10.2559	−	7.42644i	−0.977858	−	0.708083i
$111$	−1.41123			−0.133948
$112$	9.65424	−	14.1595i	0.912240	−	1.33795i
$113$	9.75845	−	9.75845i	0.917997	−	0.917997i	−0.0788863	−	0.996884i	$-0.525136\pi$
$113$	9.75845	−	9.75845i	0.917997	−	0.917997i	0.996884	+	0.0788863i	$0.0251364\pi$
$114$	−11.7409	−	4.23201i	−1.09964	−	0.396364i
$115$	−11.4185	−	3.29301i	−1.06478	−	0.307074i
$116$	−10.1682	−	8.42486i	−0.944094	−	0.782229i
$117$	−1.70005	+	6.34121i	−0.157169	+	0.586245i
$118$	−1.07252	+	0.504192i	−0.0987332	+	0.0464146i
$119$		−	4.56825i		−	0.418771i
$120$	11.9585	+	7.05884i	1.09166	+	0.644381i
$121$	5.03346			0.457587
$122$	8.03727	+	17.0969i	0.727661	+	1.54788i
$123$	7.78230	−	7.78230i	0.701706	−	0.701706i
$124$	−3.00675	+	3.62893i	−0.270014	+	0.325887i
$125$	−0.636093	+	11.1622i	−0.0568939	+	0.998380i
$126$	10.3789	+	3.74109i	0.924628	+	0.333283i
$127$	−1.79629	+	1.79629i	−0.159395	+	0.159395i	−0.782299	−	0.622904i	$-0.785953\pi$
$127$	−1.79629	+	1.79629i	−0.159395	+	0.159395i	0.622904	+	0.782299i	$0.285953\pi$
$128$	0.740364	−	11.2895i	0.0654395	−	0.997857i
$129$		−	13.4354i		−	1.18292i
$130$	7.18823	+	8.85039i	0.630450	+	0.776230i
$131$			1.17643i			0.102785i	0.998679	+	0.0513926i	$0.0163660\pi$
$131$			1.17643i			0.102785i	−0.998679	+	0.0513926i	$0.983634\pi$
$132$	−17.5067	+	1.64148i	−1.52376	+	0.142872i
$133$	−12.1765	+	12.1765i	−1.05584	+	1.05584i
$134$	−2.50692	+	6.95497i	−0.216565	+	0.600818i
$135$	1.60418	−	5.56249i	0.138066	−	0.478743i
$136$	−1.53222	−	2.59759i	−0.131387	−	0.222741i
$137$	−0.262389	+	0.262389i	−0.0224174	+	0.0224174i	−0.718227	−	0.695809i	$-0.755046\pi$
$137$	−0.262389	+	0.262389i	−0.0224174	+	0.0224174i	0.695809	+	0.718227i	$0.255046\pi$
$138$	−14.9345	+	7.02073i	−1.27131	+	0.597645i
$139$	6.48837			0.550336			0.275168	−	0.961396i	$-0.411266\pi$
$139$	6.48837			0.550336			0.275168	+	0.961396i	$0.411266\pi$
$140$	15.8341	−	10.7889i	1.33823	−	0.911830i
$141$		−	12.0233i		−	1.01255i
$142$	8.83470	+	18.7932i	0.741391	+	1.57709i
$143$	−13.9448	−	3.73854i	−1.16613	−	0.312632i
$144$	7.15643	−	1.35391i	0.596369	−	0.112826i
$145$	−7.13787	−	12.9234i	−0.592768	−	1.07323i
$146$	−3.62123	+	10.0464i	−0.299695	+	0.831447i
$147$	17.6309	−	17.6309i	1.45417	−	1.45417i
$148$	0.120004	+	1.27987i	0.00986427	+	0.105205i
$149$	23.2293			1.90302			0.951510	−	0.307617i	$-0.0995317\pi$
$149$	23.2293			1.90302			0.951510	+	0.307617i	$0.0995317\pi$
$150$	9.55931	+	12.2336i	0.780514	+	0.998872i
$151$	−6.61940			−0.538679			−0.269340	−	0.963045i	$-0.586805\pi$
$151$	−6.61940			−0.538679			−0.269340	+	0.963045i	$0.586805\pi$
$152$	−2.83970	+	11.0079i	−0.230330	+	0.892858i
$153$	1.37283	−	1.37283i	0.110987	−	0.110987i
$154$	−8.22696	+	22.8241i	−0.662947	+	1.83922i
$155$	−4.61223	+	2.54743i	−0.370463	+	0.204615i
$156$	15.6089	+	2.65441i	1.24971	+	0.212523i
$157$	5.35400	+	5.35400i	0.427296	+	0.427296i	0.887706	−	0.460410i	$-0.152298\pi$
$157$	5.35400	+	5.35400i	0.427296	+	0.427296i	−0.460410	+	0.887706i	$0.652298\pi$
$158$	−2.06954	−	4.40233i	−0.164644	−	0.350231i
$159$	−4.18286			−0.331723
$160$	5.38489	−	11.4457i	0.425713	−	0.904858i
$161$			22.7699i			1.79452i
$162$	−6.70671	−	14.2665i	−0.526929	−	1.12088i
$163$	7.39919	−	7.39919i	0.579549	−	0.579549i	−0.355230	−	0.934779i	$-0.615597\pi$
$163$	7.39919	−	7.39919i	0.579549	−	0.579549i	0.934779	+	0.355230i	$0.115597\pi$
$164$	−7.71967	−	6.39614i	−0.602805	−	0.499454i
$165$	−18.8891	−	5.44749i	−1.47052	−	0.424086i
$166$	−8.41820	−	3.03434i	−0.653379	−	0.235511i
$167$	4.82745	+	4.82745i	0.373559	+	0.373559i	0.868772	−	0.495213i	$-0.164910\pi$
$167$	4.82745	+	4.82745i	0.373559	+	0.373559i	−0.495213	+	0.868772i	$0.664910\pi$
$168$	6.64621	−	25.7636i	0.512766	−	1.98770i
$169$	11.2566	+	6.50306i	0.865889	+	0.500236i
$170$	−0.532758	−	3.32943i	−0.0408607	−	0.255356i
$171$	−7.31850			−0.559660
$172$	−12.1848	+	1.14248i	−0.929079	+	0.0871130i
$173$	−10.9705	+	10.9705i	−0.834069	+	0.834069i	−0.988071	−	0.154002i	$-0.950784\pi$
$173$	−10.9705	+	10.9705i	−0.834069	+	0.834069i	0.154002	+	0.988071i	$0.450784\pi$
$174$	−19.2867	−	6.95191i	−1.46212	−	0.527023i
$175$	20.8875	−	4.75536i	1.57895	−	0.359471i
$176$	2.97737	+	15.7376i	0.224427	+	1.18626i
$177$	−1.30105	+	1.30105i	−0.0977926	+	0.0977926i
$178$	3.79464	+	8.07197i	0.284420	+	0.605020i
$179$	−6.92372			−0.517503			−0.258752	−	0.965944i	$-0.583311\pi$
$179$	−6.92372			−0.517503			−0.258752	+	0.965944i	$0.583311\pi$
$180$	8.00067	+	1.51617i	0.596334	+	0.113009i
$181$	10.6066			0.788380			0.394190	−	0.919029i	$-0.371025\pi$
$181$	10.6066			0.788380			0.394190	+	0.919029i	$0.371025\pi$
$182$	12.4772	−	17.9326i	0.924870	−	1.32925i
$183$	20.7399	+	20.7399i	1.53313	+	1.53313i
$184$	7.63718	+	12.9474i	0.563021	+	0.954492i
$185$	−0.398251	+	1.38093i	−0.0292800	+	0.101528i
$186$	−2.48107	+	6.88324i	−0.181921	+	0.504704i
$187$	3.01897	+	3.01897i	0.220769	+	0.220769i
$188$	−10.9041	+	1.02240i	−0.795267	+	0.0745663i
$189$	−11.0923			−0.806848
$190$	−7.45446	+	10.2946i	−0.540803	+	0.746846i
$191$		−	20.7585i		−	1.50203i	−0.660283	−	0.751017i	$-0.729564\pi$
$191$		−	20.7585i		−	1.50203i	0.660283	−	0.751017i	$-0.270436\pi$
$192$	−4.86213	−	16.8788i	−0.350894	−	1.21812i
$193$	−3.53956	−	3.53956i	−0.254783	−	0.254783i	0.568145	−	0.822928i	$-0.307661\pi$
$193$	−3.53956	−	3.53956i	−0.254783	−	0.254783i	−0.822928	+	0.568145i	$0.807661\pi$
$194$	18.1493	+	6.54193i	1.30304	+	0.469683i
$195$	15.1583	+	9.14226i	1.08551	+	0.654691i
$196$	−17.4890	−	14.4905i	−1.24921	−	1.03504i
$197$	17.5499	−	17.5499i	1.25038	−	1.25038i	0.294832	−	0.955549i	$-0.404736\pi$
$197$	17.5499	−	17.5499i	1.25038	−	1.25038i	0.955549	−	0.294832i	$-0.0952636\pi$
$198$	−9.33135	+	4.38668i	−0.663150	+	0.311748i
$199$	−19.1741			−1.35922			−0.679608	−	0.733575i	$-0.737850\pi$
$199$	−19.1741			−1.35922			−0.679608	+	0.733575i	$0.737850\pi$
$200$	10.2820	−	9.70979i	0.727049	−	0.686586i
$201$			11.4780i			0.809596i
$202$	−6.22169	−	13.2348i	−0.437756	−	0.931196i
$203$	−20.0024	+	20.0024i	−1.40389	+	1.40389i
$204$	−3.60545	−	2.98729i	−0.252432	−	0.209152i
$205$	−5.41905	−	9.81141i	−0.378483	−	0.685258i
$206$	2.26108	−	6.27293i	0.157537	−	0.437056i
$207$	−6.84273	+	6.84273i	−0.475602	+	0.475602i
$208$	1.08003	−	14.3817i	0.0748866	−	0.997192i
$209$		−	16.0940i		−	1.11324i
$210$	17.4469	−	24.0940i	1.20395	−	1.66265i
$211$		−	20.6999i		−	1.42504i	−0.701653	−	0.712519i	$-0.747554\pi$
$211$		−	20.6999i		−	1.42504i	0.701653	−	0.712519i	$-0.252446\pi$
$212$	0.355690	+	3.79351i	0.0244289	+	0.260539i
$213$	22.7976	+	22.7976i	1.56206	+	1.56206i
$214$	−14.6553	−	5.28253i	−1.00182	−	0.361106i
$215$	−13.1469	−	3.79148i	−0.896613	−	0.258577i
$216$	−6.30729	+	3.72044i	−0.429157	+	0.253144i
$217$	7.13864	+	7.13864i	0.484603	+	0.484603i
$218$	1.90581	+	4.05405i	0.129078	+	0.274575i
$219$			16.5799i			1.12037i
$220$	−3.33418	+	17.5941i	−0.224791	+	1.18619i
$221$	−1.92176	−	3.32964i	−0.129272	−	0.223976i
$222$	0.849077	+	1.80616i	0.0569863	+	0.121221i
$223$	−5.91543	+	5.91543i	−0.396126	+	0.396126i	−0.876864	−	0.480738i	$-0.840369\pi$
$223$	−5.91543	+	5.91543i	−0.396126	+	0.396126i	0.480738	+	0.876864i	$0.340369\pi$
$224$	−23.9306	−	3.83676i	−1.59893	−	0.256354i
$225$	7.70610	+	4.84797i	0.513740	+	0.323198i
$226$	−18.3606	−	6.61807i	−1.22133	−	0.440228i
$227$	−0.579078	−	0.579078i	−0.0384347	−	0.0384347i	0.687628	−	0.726063i	$-0.258652\pi$
$227$	−0.579078	−	0.579078i	−0.0384347	−	0.0384347i	−0.726063	+	0.687628i	$0.758652\pi$
$228$	1.64767	+	17.5728i	0.109120	+	1.16378i
$229$	−5.64962			−0.373337			−0.186669	−	0.982423i	$-0.559769\pi$
$229$	−5.64962			−0.373337			−0.186669	+	0.982423i	$0.559769\pi$
$230$	2.65547	+	16.5952i	0.175096	+	1.09425i
$231$			37.6673i			2.47833i
$232$	−4.66476	+	18.0826i	−0.306257	+	1.18718i
$233$	−5.44699	+	5.44699i	−0.356844	+	0.356844i	−0.862648	−	0.505804i	$-0.831196\pi$
$233$	−5.44699	+	5.44699i	−0.356844	+	0.356844i	0.505804	+	0.862648i	$0.331196\pi$
$234$	9.13863	−	1.63944i	0.597411	−	0.107173i
$235$	−11.7652	−	3.39300i	−0.767477	−	0.221335i
$236$	1.29058	+	1.06931i	0.0840093	+	0.0696060i
$237$	−5.34037	−	5.34037i	−0.346894	−	0.346894i
$238$	−5.84666	+	2.74852i	−0.378983	+	0.178160i
$239$		−	1.73850i		−	0.112454i	−0.998418	−	0.0562272i	$-0.982093\pi$
$239$		−	1.73850i		−	0.112454i	0.998418	−	0.0562272i	$-0.0179071\pi$
$240$	1.83930	−	19.5521i	0.118726	−	1.26208i
$241$		−	1.91871i		−	0.123595i	−0.998089	−	0.0617976i	$-0.980317\pi$
$241$		−	1.91871i		−	0.123595i	0.998089	−	0.0617976i	$-0.0196833\pi$
$242$	−3.02842	−	6.44206i	−0.194674	−	0.414111i
$243$	−11.8143	−	11.8143i	−0.757887	−	0.757887i
$244$	17.0457	−	20.5730i	1.09124	−	1.31705i
$245$	−12.2769	−	22.2278i	−0.784343	−	1.42008i
$246$	−14.6424	−	5.27787i	−0.933567	−	0.336505i
$247$	−3.75265	+	13.9975i	−0.238775	+	0.890636i
$248$	6.45351	+	1.66481i	0.409798	+	0.105715i
$249$	−13.8928			−0.880421
$250$	14.6687	−	5.90174i	0.927727	−	0.373259i
$251$			28.0828i			1.77257i	0.463139	+	0.886285i	$0.346723\pi$
$251$			28.0828i			1.77257i	−0.463139	+	0.886285i	$0.653277\pi$
$252$	−1.45654	−	15.5343i	−0.0917532	−	0.978569i
$253$	−15.0477	−	15.0477i	−0.946041	−	0.946041i
$254$	3.37973	+	1.21823i	0.212063	+	0.0764383i
$255$	−2.53095	−	4.58239i	−0.158494	−	0.286960i
$256$	−14.8942	+	5.84484i	−0.930889	+	0.365302i
$257$	13.3998	+	13.3998i	0.835854	+	0.835854i	0.988310	−	0.152456i	$-0.0487183\pi$
$257$	13.3998	+	13.3998i	0.835854	+	0.835854i	−0.152456	+	0.988310i	$0.548718\pi$
$258$	−17.1952	+	8.08348i	−1.07053	+	0.503256i
$259$	2.75376			0.171110
$260$	7.00229	−	14.5247i	0.434263	−	0.900786i
$261$	−12.0221			−0.744147
$262$	1.50565	−	0.707809i	0.0930195	−	0.0437286i
$263$	−5.22835	−	5.22835i	−0.322394	−	0.322394i	0.527291	−	0.849685i	$-0.323208\pi$
$263$	−5.22835	−	5.22835i	−0.322394	−	0.322394i	−0.849685	+	0.527291i	$0.823208\pi$
$264$	12.6339	+	21.4183i	0.777562	+	1.31821i
$265$	−1.18041	+	4.09307i	−0.0725121	+	0.251435i
$266$	22.9102	+	8.25800i	1.40472	+	0.506331i
$267$	9.79192	+	9.79192i	0.599256	+	0.599256i
$268$	10.4096	−	0.976032i	0.635868	−	0.0596207i
$269$			5.29424i			0.322796i	0.986889	+	0.161398i	$0.0516002\pi$
$269$			5.29424i			0.322796i	−0.986889	+	0.161398i	$0.948400\pi$
$270$	−8.08431	+	1.29361i	−0.491995	+	0.0787265i
$271$	20.2679			1.23119			0.615594	−	0.788063i	$-0.288916\pi$
$271$	20.2679			1.23119			0.615594	+	0.788063i	$0.288916\pi$
$272$	−2.40264	+	3.52387i	−0.145681	+	0.213666i
$273$	8.78293	−	32.7605i	0.531567	−	1.98276i
$274$	0.493686	+	0.177949i	0.0298246	+	0.0107503i
$275$	−10.6611	+	16.9463i	−0.642887	+	1.02190i
$276$	17.9709	+	14.8898i	1.08172	+	0.896262i
$277$	−16.0235	−	16.0235i	−0.962759	−	0.962759i	0.0365721	−	0.999331i	$-0.488356\pi$
$277$	−16.0235	−	16.0235i	−0.962759	−	0.962759i	−0.999331	+	0.0365721i	$0.988356\pi$
$278$	−3.90378	−	8.30412i	−0.234133	−	0.498048i
$279$			4.29056i			0.256869i
$280$	−23.3349	−	13.7740i	−1.39453	−	0.823157i
$281$		−	15.1928i		−	0.906329i	−0.891427	−	0.453164i	$-0.850295\pi$
$281$		−	15.1928i		−	0.906329i	0.891427	−	0.453164i	$-0.149705\pi$
$282$	−15.3880	+	7.23391i	−0.916342	+	0.430773i
$283$	13.4327	+	13.4327i	0.798488	+	0.798488i	0.982857	−	0.184369i	$-0.0590241\pi$
$283$	13.4327	+	13.4327i	0.798488	+	0.798488i	−0.184369	+	0.982857i	$0.559024\pi$
$284$	18.7369	−	22.6141i	1.11183	−	1.34190i
$285$	−5.46804	+	18.9604i	−0.323899	+	1.12312i
$286$	3.60525	+	20.0966i	0.213183	+	1.18834i
$287$	−15.1857	+	15.1857i	−0.896386	+	0.896386i
$288$	−6.03852	−	8.34454i	−0.355823	−	0.491707i
$289$		−	15.8631i		−	0.933124i
$290$	−12.2454	+	16.9108i	−0.719075	+	0.993038i
$291$	29.9524			1.75584
$292$	15.0366	−	1.40987i	0.879951	−	0.0825065i
$293$	−8.51447	−	8.51447i	−0.497421	−	0.497421i	0.413213	−	0.910634i	$-0.364406\pi$
$293$	−8.51447	−	8.51447i	−0.497421	−	0.497421i	−0.910634	+	0.413213i	$0.864406\pi$
$294$	−33.1726	−	11.9571i	−1.93466	−	0.697351i
$295$	0.905958	+	1.64027i	0.0527469	+	0.0955004i
$296$	1.56584	−	0.923630i	0.0910123	−	0.0536849i
$297$	7.33047	−	7.33047i	0.425357	−	0.425357i
$298$	−13.9761	−	29.7300i	−0.809614	−	1.72221i
$299$	9.57880	+	16.5962i	0.553956	+	0.959782i
$300$	9.90575	−	19.5949i	0.571909	−	1.13131i
$301$			26.2167i			1.51110i
$302$	3.98261	+	8.47182i	0.229174	+	0.487499i
$303$	−16.0548	−	16.0548i	−0.922325	−	0.922325i
$304$	15.7969	−	2.98860i	0.906017	−	0.171408i
$305$	26.1474	−	14.4418i	1.49720	−	0.826935i
$306$	−2.58299	−	0.931041i	−0.147660	−	0.0532241i
$307$	−6.65969	−	6.65969i	−0.380088	−	0.380088i	0.491045	−	0.871134i	$-0.336615\pi$
$307$	−6.65969	−	6.65969i	−0.380088	−	0.380088i	−0.871134	+	0.491045i	$0.836615\pi$
$308$	34.1612	−	3.20304i	1.94651	−	0.182510i
$309$		−	10.3524i		−	0.588929i
$310$	6.03531	+	4.37027i	0.342783	+	0.248214i
$311$		−	18.3677i		−	1.04154i	−0.853698	−	0.520768i	$-0.825646\pi$
$311$		−	18.3677i		−	1.04154i	0.853698	−	0.520768i	$-0.174354\pi$
$312$	−5.99397	−	21.5741i	−0.339342	−	1.22139i
$313$	−1.25695	+	1.25695i	−0.0710469	+	0.0710469i	−0.741737	−	0.670690i	$-0.765998\pi$
$313$	−1.25695	+	1.25695i	−0.0710469	+	0.0710469i	0.670690	+	0.741737i	$0.265998\pi$
$314$	3.63103	−	10.0736i	0.204911	−	0.568485i
$315$	4.83374	−	16.7610i	0.272350	−	0.944373i
$316$	−4.38916	+	5.29740i	−0.246909	+	0.298002i
$317$	−0.304766	+	0.304766i	−0.0171174	+	0.0171174i	−0.715614	−	0.698496i	$-0.753853\pi$
$317$	−0.304766	+	0.304766i	−0.0171174	+	0.0171174i	0.698496	+	0.715614i	$0.253853\pi$
$318$	2.51665	+	5.35342i	0.141127	+	0.300205i
$319$		−	26.4375i		−	1.48022i
$320$	−17.8885	−	0.00547717i	−1.00000	−	0.000306183i
$321$	−24.1862			−1.34994
$322$	29.1420	−	13.6997i	1.62402	−	0.763454i
$323$	3.03036	−	3.03036i	0.168614	−	0.168614i
$324$	−14.2238	+	17.1671i	−0.790213	+	0.953730i
$325$	13.2237	−	12.2529i	0.733518	−	0.679670i
$326$	−13.9216	−	5.01805i	−0.771046	−	0.277924i
$327$	4.91787	+	4.91787i	0.271959	+	0.271959i
$328$	−3.54148	+	13.7283i	−0.195545	+	0.758017i
$329$			23.4613i			1.29346i
$330$	4.39283	+	27.4527i	0.241818	+	1.51122i
$331$	−1.54670			−0.0850143			−0.0425071	−	0.999096i	$-0.513535\pi$
$331$	−1.54670			−0.0850143			−0.0425071	+	0.999096i	$0.513535\pi$
$332$	1.18138	+	12.5996i	0.0648364	+	0.691495i
$333$	0.827549	+	0.827549i	0.0453494	+	0.0453494i
$334$	3.27392	−	9.08286i	0.179141	−	0.496992i
$335$	11.2316	+	3.23911i	0.613648	+	0.176972i
$336$	−36.9722	+	6.99471i	−2.01700	+	0.381593i
$337$	21.3686	+	21.3686i	1.16402	+	1.16402i	0.983587	+	0.180434i	$0.0577502\pi$
$337$	21.3686	+	21.3686i	1.16402	+	1.16402i	0.180434	+	0.983587i	$0.442250\pi$
$338$	1.55033	−	18.3193i	0.0843270	−	0.996438i
$339$	−30.3010			−1.64573
$340$	−3.94063	+	2.68503i	−0.213710	+	0.145616i
$341$	−9.43528			−0.510949
$342$	4.40323	+	9.36656i	0.238099	+	0.506485i
$343$	−13.1968	+	13.1968i	−0.712559	+	0.712559i
$344$	8.79325	+	14.9072i	0.474100	+	0.803745i
$345$	12.6152	+	22.8404i	0.679181	+	1.22968i
$346$	20.6410	+	7.44005i	1.10967	+	0.399980i
$347$	15.8528	−	15.8528i	0.851025	−	0.851025i	−0.139235	−	0.990259i	$-0.544464\pi$
$347$	15.8528	−	15.8528i	0.851025	−	0.851025i	0.990259	+	0.139235i	$0.0444643\pi$
$348$	2.70662	+	28.8667i	0.145090	+	1.54742i
$349$	5.85768			0.313554			0.156777	−	0.987634i	$-0.449890\pi$
$349$	5.85768			0.313554			0.156777	+	0.987634i	$0.449890\pi$
$350$	−18.6533	−	23.8717i	−0.997058	−	1.27600i
$351$	−8.08480	+	4.66630i	−0.431535	+	0.249068i
$352$	18.3503	−	13.2792i	0.978075	−	0.707783i
$353$	11.5440	+	11.5440i	0.614427	+	0.614427i	0.944096	−	0.329669i	$-0.106937\pi$
$353$	11.5440	+	11.5440i	0.614427	+	0.614427i	−0.329669	+	0.944096i	$0.606937\pi$
$354$	2.44792	+	0.882356i	0.130106	+	0.0468967i
$355$	28.7417	−	15.8747i	1.52545	−	0.842539i
$356$	8.04781	−	9.71312i	0.426533	−	0.514794i
$357$	−7.09245	+	7.09245i	−0.375372	+	0.375372i
$358$	4.16571	+	8.86130i	0.220164	+	0.468334i
$359$			10.8120i			0.570635i	0.958433	+	0.285317i	$0.0920990\pi$
$359$			10.8120i			0.570635i	−0.958433	+	0.285317i	$0.907901\pi$
$360$	−2.87319	−	11.1518i	−0.151431	−	0.587754i
$361$	2.84531			0.149753
$362$	−6.38152	−	13.5748i	−0.335405	−	0.713475i
$363$	−7.81472	−	7.81472i	−0.410166	−	0.410166i
$364$	−30.4579	−	5.17960i	−1.59643	−	0.271485i
$365$	16.2240	+	4.67888i	0.849201	+	0.244904i
$366$	14.0656	−	39.0221i	0.735218	−	2.03972i
$367$	−6.69338	+	6.69338i	−0.349392	+	0.349392i	−0.859883	−	0.510491i	$-0.829464\pi$
$367$	−6.69338	+	6.69338i	−0.349392	+	0.349392i	0.510491	+	0.859883i	$0.329464\pi$
$368$	11.9757	−	17.5643i	0.624275	−	0.915603i
$369$	−9.12713			−0.475139
$370$	2.00700	−	0.321149i	0.104339	−	0.0166957i
$371$	8.16210			0.423755
$372$	10.3022	−	0.965966i	0.534147	−	0.0500830i
$373$	26.8369	−	26.8369i	1.38956	−	1.38956i	0.563337	−	0.826227i	$-0.309517\pi$
$373$	26.8369	−	26.8369i	1.38956	−	1.38956i	0.826227	−	0.563337i	$-0.190483\pi$
$374$	2.04743	−	5.68021i	0.105870	−	0.293717i
$375$	18.3175	−	16.3424i	0.945913	−	0.843917i
$376$	7.86908	+	13.3405i	0.405817	+	0.687984i
$377$	−6.16446	+	22.9936i	−0.317486	+	1.18423i
$378$	6.67378	+	14.1965i	0.343262	+	0.730188i
$379$			6.51205i			0.334501i	0.985914	+	0.167251i	$0.0534889\pi$
$379$			6.51205i			0.334501i	−0.985914	+	0.167251i	$0.946511\pi$
$380$	17.6605	+	3.34677i	0.905964	+	0.171685i
$381$	5.57768			0.285753
$382$	−26.5677	+	12.4895i	−1.35932	+	0.639020i
$383$	6.37394	−	6.37394i	0.325693	−	0.325693i	−0.525253	−	0.850946i	$-0.676029\pi$
$383$	6.37394	−	6.37394i	0.325693	−	0.325693i	0.850946	+	0.525253i	$0.176029\pi$
$384$	−18.6769	+	16.3780i	−0.953104	+	0.835788i
$385$	36.8587	+	10.6298i	1.87849	+	0.541744i
$386$	−2.40049	+	6.65969i	−0.122182	+	0.338969i
$387$	−7.87853	+	7.87853i	−0.400488	+	0.400488i
$388$	−2.54700	−	27.1643i	−0.129304	−	1.37906i
$389$			31.2025i			1.58203i	0.611797	+	0.791015i	$0.290447\pi$
$389$			31.2025i			1.58203i	−0.611797	+	0.791015i	$0.709553\pi$
$390$	2.58059	−	24.9008i	0.130673	−	1.26090i
$391$		−	5.66672i		−	0.286578i
$392$	−8.02325	+	31.1016i	−0.405235	+	1.57087i
$393$	1.82647	−	1.82647i	0.0921333	−	0.0921333i
$394$	−33.0203	−	11.9022i	−1.66354	−	0.599623i
$395$	−6.73279	+	3.71866i	−0.338763	+	0.187106i
$396$	11.2285	+	9.30342i	0.564256	+	0.467514i
$397$	7.96092	−	7.96092i	0.399547	−	0.399547i	−0.478526	−	0.878073i	$-0.658829\pi$
$397$	7.96092	−	7.96092i	0.399547	−	0.399547i	0.878073	+	0.478526i	$0.158829\pi$
$398$	11.5362	+	24.5399i	0.578260	+	1.23007i
$399$	37.8095			1.89284
$400$	−18.6133	−	7.31744i	−0.930665	−	0.365872i
$401$			34.8531i			1.74048i	0.492629	+	0.870239i	$0.336036\pi$
$401$			34.8531i			1.74048i	−0.492629	+	0.870239i	$0.663964\pi$
$402$	14.6901	−	6.90583i	0.732675	−	0.344431i
$403$	8.20617	+	2.20003i	0.408779	+	0.109592i
$404$	−13.1952	+	15.9256i	−0.656484	+	0.792329i
$405$	−21.8188	+	12.0510i	−1.08418	+	0.598818i
$406$	37.6345	+	13.5654i	1.86777	+	0.673239i
$407$	−1.81985	+	1.81985i	−0.0902065	+	0.0902065i
$408$	−1.65403	+	6.41175i	−0.0818869	+	0.317429i
$409$	−21.4960			−1.06291			−0.531454	−	0.847087i	$-0.678354\pi$
$409$	−21.4960			−1.06291			−0.531454	+	0.847087i	$0.678354\pi$
$410$	−9.29669	+	12.8387i	−0.459131	+	0.634056i
$411$	0.814745			0.0401884
$412$	−9.38879	+	0.880319i	−0.462553	+	0.0433702i
$413$	2.53875	−	2.53875i	0.124924	−	0.124924i
$414$	12.8746	+	4.64066i	0.632753	+	0.228076i
$415$	−3.92057	+	13.5946i	−0.192453	+	0.667331i
$416$	−19.0562	+	7.27059i	−0.934307	+	0.356470i
$417$	−10.0735	−	10.0735i	−0.493303	−	0.493303i
$418$	−20.5978	+	9.68305i	−1.00747	+	0.473614i
$419$	14.2968			0.698445			0.349222	−	0.937040i	$-0.386446\pi$
$419$	14.2968			0.698445			0.349222	+	0.937040i	$0.386446\pi$
$420$	−41.3337	−	7.83298i	−2.01688	−	0.382210i
$421$		−	33.3634i		−	1.62603i	−0.582241	−	0.813016i	$-0.697824\pi$
$421$		−	33.3634i		−	1.62603i	0.582241	−	0.813016i	$-0.302176\pi$
$422$	−26.4927	+	12.4542i	−1.28964	+	0.606263i
$423$	−7.05050	+	7.05050i	−0.342807	+	0.342807i
$424$	4.64111	−	2.73762i	0.225392	−	0.132951i
$425$	−5.19825	+	1.18346i	−0.252152	+	0.0574062i
$426$	15.4611	−	42.8938i	0.749092	−	2.07821i
$427$	−40.4701	−	40.4701i	−1.95848	−	1.95848i
$428$	2.05667	+	21.9349i	0.0994130	+	1.06026i
$429$	15.8458	+	27.4544i	0.765043	+	1.32551i
$430$	3.05744	+	19.1072i	0.147443	+	0.921432i
$431$	3.59162			0.173002			0.0865011	−	0.996252i	$-0.472431\pi$
$431$	3.59162			0.173002			0.0865011	+	0.996252i	$0.472431\pi$
$432$	8.55643	+	5.83393i	0.411671	+	0.280685i
$433$	−13.7981	+	13.7981i	−0.663094	+	0.663094i	−0.956108	−	0.293014i	$-0.905342\pi$
$433$	−13.7981	+	13.7981i	−0.663094	+	0.663094i	0.293014	+	0.956108i	$0.405342\pi$
$434$	4.84135	−	13.4314i	0.232392	−	0.644727i
$435$	−8.98233	+	31.1462i	−0.430670	+	1.49334i
$436$	4.04191	−	4.87830i	0.193573	−	0.233628i
$437$	−15.1045	+	15.1045i	−0.722546	+	0.722546i
$438$	21.2197	−	9.97542i	1.01392	−	0.476644i
$439$	−17.0950			−0.815898			−0.407949	−	0.913005i	$-0.633756\pi$
$439$	−17.0950			−0.815898			−0.407949	+	0.913005i	$0.633756\pi$
$440$	24.5238	−	6.31838i	1.16913	−	0.301217i
$441$	−20.6776			−0.984647
$442$	−3.10518	+	4.46286i	−0.147698	+	0.212277i
$443$	1.06840	+	1.06840i	0.0507610	+	0.0507610i	0.732032	−	0.681271i	$-0.238572\pi$
$443$	1.06840	+	1.06840i	0.0507610	+	0.0507610i	−0.681271	+	0.732032i	$0.738572\pi$
$444$	1.80075	−	2.17338i	0.0854599	−	0.103144i
$445$	12.3450	−	6.81841i	0.585210	−	0.323224i
$446$	11.1299	+	4.01178i	0.527016	+	0.189963i
$447$	−36.0648	−	36.0648i	−1.70580	−	1.70580i
$448$	9.48755	+	32.9359i	0.448245	+	1.55608i
$449$	−8.23041			−0.388417			−0.194208	−	0.980960i	$-0.562214\pi$
$449$	−8.23041			−0.388417			−0.194208	+	0.980960i	$0.562214\pi$
$450$	1.56823	−	12.7794i	0.0739272	−	0.602429i
$451$		−	20.0713i		−	0.945120i
$452$	2.57665	+	27.4805i	0.121195	+	1.29257i
$453$	10.2770	+	10.2770i	0.482855	+	0.482855i
$454$	−0.392724	+	1.08954i	−0.0184315	+	0.0511345i
$455$	−29.5787	−	17.8395i	−1.38667	−	0.836327i
$456$	21.4991	−	12.6816i	1.00679	−	0.593868i
$457$	12.8554	−	12.8554i	0.601350	−	0.601350i	−0.339321	−	0.940671i	$-0.610197\pi$
$457$	12.8554	−	12.8554i	0.601350	−	0.601350i	0.940671	+	0.339321i	$0.110197\pi$
$458$	3.39913	+	7.23064i	0.158831	+	0.337866i
$459$	2.76053			0.128851
$460$	19.6416	−	13.3832i	0.915794	−	0.623995i
$461$		−	14.8290i		−	0.690654i	−0.938482	−	0.345327i	$-0.887768\pi$
$461$		−	14.8290i		−	0.690654i	0.938482	−	0.345327i	$-0.112232\pi$
$462$	48.2084	−	22.6628i	2.24286	−	1.05437i
$463$	19.1031	−	19.1031i	0.887795	−	0.887795i	−0.106516	−	0.994311i	$-0.533969\pi$
$463$	19.1031	−	19.1031i	0.887795	−	0.887795i	0.994311	+	0.106516i	$0.0339694\pi$
$464$	25.9496	−	4.90936i	1.20468	−	0.227912i
$465$	11.1158	+	3.20571i	0.515481	+	0.148661i
$466$	10.2485	+	3.69409i	0.474754	+	0.171125i
$467$	−2.71966	+	2.71966i	−0.125851	+	0.125851i	−0.767227	−	0.641376i	$-0.778364\pi$
$467$	−2.71966	+	2.71966i	−0.125851	+	0.125851i	0.641376	+	0.767227i	$0.278364\pi$
$468$	−7.59655	−	10.7097i	−0.351151	−	0.495054i
$469$		−	22.3972i		−	1.03421i
$470$	2.73610	+	17.0991i	0.126207	+	0.788721i
$471$		−	16.6248i		−	0.766028i
$472$	0.592064	−	2.29510i	0.0272520	−	0.105640i
$473$	−17.3255	−	17.3255i	−0.796628	−	0.796628i
$474$	−3.62178	+	10.0479i	−0.166354	+	0.461517i
$475$	17.0103	+	10.7013i	0.780485	+	0.491010i
$476$	7.03538	+	5.82916i	0.322466	+	0.267179i
$477$	2.45284	+	2.45284i	0.112308	+	0.112308i
$478$	−2.22502	+	1.04598i	−0.101770	+	0.0478422i
$479$			13.9163i			0.635854i	0.948115	+	0.317927i	$0.102987\pi$
$479$			13.9163i			0.635854i	−0.948115	+	0.317927i	$0.897013\pi$
$480$	−26.1303	+	9.40965i	−1.19268	+	0.429490i
$481$	2.00712	−	1.15845i	0.0915167	−	0.0528206i
$482$	−2.45566	+	1.15441i	−0.111852	+	0.0525818i
$483$	35.3515	−	35.3515i	1.60855	−	1.60855i
$484$	−6.42278	+	7.75183i	−0.291945	+	0.352356i
$485$	8.45261	−	29.3094i	0.383813	−	1.33087i
$486$	−8.01233	+	22.2286i	−0.363447	+	1.00831i
$487$	14.0817	+	14.0817i	0.638104	+	0.638104i	0.950088	−	0.311983i	$-0.100993\pi$
$487$	14.0817	+	14.0817i	0.638104	+	0.638104i	−0.311983	+	0.950088i	$0.600993\pi$
$488$	−36.5859	−	9.43805i	−1.65617	−	0.427240i
$489$	−22.9753			−1.03898
$490$	−21.0617	+	29.0861i	−0.951472	+	1.31398i
$491$			5.72122i			0.258195i	0.991632	+	0.129097i	$0.0412080\pi$
$491$			5.72122i			0.258195i	−0.991632	+	0.129097i	$0.958792\pi$
$492$	2.05486	+	21.9155i	0.0926402	+	0.988029i
$493$	4.97797	−	4.97797i	0.224196	−	0.224196i
$494$	20.1724	−	3.61886i	0.907599	−	0.162820i
$495$	7.88221	+	14.2711i	0.354279	+	0.641436i
$496$	−1.75210	−	9.26115i	−0.0786718	−	0.415838i
$497$	−44.4854	−	44.4854i	−1.99544	−	1.99544i
$498$	8.35872	+	17.7807i	0.374563	+	0.796771i
$499$			18.6310i			0.834040i	0.908897	+	0.417020i	$0.136926\pi$
$499$			18.6310i			0.834040i	−0.908897	+	0.417020i	$0.863074\pi$
$500$	−16.3788	−	15.2228i	−0.732484	−	0.680785i
$501$		−	14.9897i		−	0.669692i
$502$	35.9417	−	16.8962i	1.60416	−	0.754116i
$503$	−7.95573	−	7.95573i	−0.354728	−	0.354728i	0.507137	−	0.861865i	$-0.330704\pi$
$503$	−7.95573	−	7.95573i	−0.354728	−	0.354728i	−0.861865	+	0.507137i	$0.830704\pi$
$504$	−19.0052	+	11.2105i	−0.846558	+	0.499354i
$505$	−20.2408	+	11.1795i	−0.900706	+	0.497479i
$506$	−10.2052	+	28.3123i	−0.453676	+	1.25864i
$507$	−7.38006	−	27.5728i	−0.327760	−	1.22455i
$508$	−0.474298	−	5.05849i	−0.0210436	−	0.224434i
$509$	4.08878			0.181232			0.0906160	−	0.995886i	$-0.471116\pi$
$509$	4.08878			0.181232			0.0906160	+	0.995886i	$0.471116\pi$
$510$	−4.34199	+	5.99626i	−0.192266	+	0.265519i
$511$		−	32.3527i		−	1.43120i
$512$	16.4417	+	15.5457i	0.726628	+	0.687031i
$513$	−7.35813	−	7.35813i	−0.324869	−	0.324869i
$514$	9.08757	−	25.2117i	0.400836	−	1.11204i
$515$	−10.1302	−	2.92147i	−0.446389	−	0.128735i
$516$	20.6912	+	17.1437i	0.910881	+	0.754711i
$517$	−15.5046	−	15.5046i	−0.681892	−	0.681892i
$518$	−1.65682	−	3.52439i	−0.0727965	−	0.154853i
$519$	34.0645			1.49526
$520$	−22.8024	−	0.222938i	−0.999952	−	0.00977648i
$521$	14.0359			0.614924			0.307462	−	0.951560i	$-0.400520\pi$
$521$	14.0359			0.614924			0.307462	+	0.951560i	$0.400520\pi$
$522$	7.23317	+	15.3864i	0.316587	+	0.673445i
$523$	13.6052	+	13.6052i	0.594912	+	0.594912i	0.938954	−	0.344042i	$-0.111796\pi$
$523$	13.6052	+	13.6052i	0.594912	+	0.594912i	−0.344042	+	0.938954i	$0.611796\pi$
$524$	−1.81177	−	1.50115i	−0.0791477	−	0.0655778i
$525$	−39.8119	−	25.0460i	−1.73753	−	1.09310i
$526$	−3.54581	+	9.83716i	−0.154605	+	0.428921i
$527$	−1.77659	−	1.77659i	−0.0773893	−	0.0773893i
$528$	19.8109	−	29.0559i	0.862158	−	1.26450i
$529$			5.24510i			0.228048i
$530$	5.94870	−	0.951879i	0.258395	−	0.0413470i
$531$	1.52587			0.0662173
$532$	−3.21513	−	34.2901i	−0.139393	−	1.48666i
$533$	−4.68004	+	17.4567i	−0.202715	+	0.756132i
$534$	6.64078	−	18.4235i	0.287375	−	0.797265i
$535$	−6.82538	+	23.6670i	−0.295087	+	1.02321i
$536$	−7.51219	−	12.7355i	−0.324477	−	0.550088i
$537$	10.7494	+	10.7494i	0.463873	+	0.463873i
$538$	6.77582	−	3.18532i	0.292126	−	0.137329i
$539$		−	45.4717i		−	1.95860i
$540$	6.51961	+	9.56837i	0.280559	+	0.411757i
$541$		−	20.5892i		−	0.885200i	−0.896719	−	0.442600i	$-0.854056\pi$
$541$		−	20.5892i		−	0.885200i	0.896719	−	0.442600i	$-0.145944\pi$
$542$	−12.1943	−	25.9398i	−0.523792	−	1.11421i
$543$	−16.4673	−	16.4673i	−0.706678	−	0.706678i
$544$	5.95558	+	0.954850i	0.255343	+	0.0409388i
$545$	6.20013	−	3.42447i	0.265584	−	0.146688i
$546$	−47.2128	+	8.46980i	−2.02052	+	0.362474i
$547$	−27.5630	+	27.5630i	−1.17851	+	1.17851i	−0.198387	+	0.980124i	$0.563570\pi$
$547$	−27.5630	+	27.5630i	−1.17851	+	1.17851i	−0.980124	+	0.198387i	$0.936430\pi$
$548$	−0.0692819	−	0.738906i	−0.00295957	−	0.0315645i
$549$		−	24.3238i		−	1.03812i
$550$	28.1030	+	3.44867i	1.19832	+	0.147052i
$551$	−26.5373			−1.13052
$552$	8.24434	−	31.9586i	0.350902	−	1.36025i
$553$	10.4208	+	10.4208i	0.443136	+	0.443136i
$554$	−10.8670	+	30.1483i	−0.461693	+	1.28088i
$555$	2.76228	−	1.52567i	0.117252	−	0.0647610i
$556$	−8.27927	+	9.99247i	−0.351119	+	0.423775i
$557$	−14.7124	+	14.7124i	−0.623382	+	0.623382i	−0.946395	−	0.323012i	$-0.895304\pi$
$557$	−14.7124	+	14.7124i	−0.623382	+	0.623382i	0.323012	+	0.946395i	$0.395304\pi$
$558$	5.49126	−	2.58145i	0.232463	−	0.109281i
$559$	11.0288	+	19.1084i	0.466467	+	0.808199i
$560$	−3.58905	+	38.1524i	−0.151665	+	1.61223i
$561$		−	9.37423i		−	0.395780i
$562$	−19.4445	+	9.14088i	−0.820217	+	0.385585i
$563$	−9.04527	−	9.04527i	−0.381213	−	0.381213i	0.490326	−	0.871539i	$-0.336878\pi$
$563$	−9.04527	−	9.04527i	−0.381213	−	0.381213i	−0.871539	+	0.490326i	$0.836878\pi$
$564$	18.5166	+	15.3419i	0.779690	+	0.646012i
$565$	−8.55100	+	29.6505i	−0.359743	+	1.24741i
$566$	9.10988	−	25.2736i	0.382917	−	1.06233i
$567$	33.7703	+	33.7703i	1.41822	+	1.41822i
$568$	−40.2158	−	10.3745i	−1.68742	−	0.435302i
$569$		−	16.7114i		−	0.700577i	−0.936642	−	0.350289i	$-0.886083\pi$
$569$		−	16.7114i		−	0.700577i	0.936642	−	0.350289i	$-0.113917\pi$
$570$	27.5563	−	4.40941i	1.15421	−	0.184690i
$571$			12.2500i			0.512646i	0.966591	+	0.256323i	$0.0825111\pi$
$571$			12.2500i			0.512646i	−0.966591	+	0.256323i	$0.917489\pi$
$572$	23.5514	−	16.7054i	0.984734	−	0.698489i
$573$	−32.2287	+	32.2287i	−1.34637	+	1.34637i
$574$	28.5720	+	10.2988i	1.19257	+	0.429864i
$575$	25.9101	−	5.89882i	1.08052	−	0.245998i
$576$	−7.04661	+	12.7489i	−0.293609	+	0.531206i
$577$	28.8920	−	28.8920i	1.20279	−	1.20279i	0.229473	−	0.973315i	$-0.426300\pi$
$577$	28.8920	−	28.8920i	1.20279	−	1.20279i	0.973315	−	0.229473i	$-0.0737004\pi$
$578$	−20.3023	+	9.54416i	−0.844466	+	0.396985i
$579$			10.9907i			0.456758i
$580$	29.0108	+	5.49772i	1.20461	+	0.228280i
$581$	27.1093			1.12468
$582$	−18.0211	−	38.3344i	−0.746997	−	1.58901i
$583$	−5.39400	+	5.39400i	−0.223397	+	0.223397i
$584$	−10.8513	−	18.3963i	−0.449030	−	0.761244i
$585$	−3.52782	−	14.2499i	−0.145858	−	0.589161i
$586$	−5.77442	+	16.0200i	−0.238539	+	0.661781i
$587$	−4.79794	−	4.79794i	−0.198032	−	0.198032i	0.601124	−	0.799156i	$-0.294720\pi$
$587$	−4.79794	−	4.79794i	−0.198032	−	0.198032i	−0.799156	+	0.601124i	$0.794720\pi$
$588$	4.65531	+	49.6499i	0.191982	+	2.04753i
$589$			9.47088i			0.390241i
$590$	1.55422	−	2.14637i	0.0639863	−	0.0883647i
$591$	−54.4944			−2.24160
$592$	−2.12420	−	1.44832i	−0.0873041	−	0.0595256i
$593$	−14.6931	−	14.6931i	−0.603373	−	0.603373i	0.337833	−	0.941206i	$-0.390306\pi$
$593$	−14.6931	−	14.6931i	−0.603373	−	0.603373i	−0.941206	+	0.337833i	$0.890306\pi$
$594$	−13.7923	−	4.97144i	−0.565905	−	0.203981i
$595$	4.93869	+	8.94169i	0.202467	+	0.366574i
$596$	−29.6410	+	35.7745i	−1.21414	+	1.46538i
$597$	29.7688	+	29.7688i	1.21836	+	1.21836i
$598$	15.4774	−	22.2446i	0.632918	−	0.909650i
$599$	38.2891			1.56445			0.782226	−	0.622995i	$-0.214084\pi$
$599$	38.2891			1.56445			0.782226	+	0.622995i	$0.214084\pi$
$600$	−31.0384	−	0.888418i	−1.26714	−	0.0362695i
$601$	−16.2330			−0.662159			−0.331079	−	0.943603i	$-0.607413\pi$
$601$	−16.2330			−0.662159			−0.331079	+	0.943603i	$0.607413\pi$
$602$	33.5533	−	15.7735i	1.36753	−	0.642878i
$603$	6.73074	−	6.73074i	0.274097	−	0.274097i
$604$	8.44647	−	10.1943i	0.343682	−	0.414799i
$605$	−9.85228	+	5.44163i	−0.400552	+	0.221234i
$606$	−10.8882	+	30.2072i	−0.442303	+	1.22708i
$607$	6.35320	−	6.35320i	0.257868	−	0.257868i	−0.566318	−	0.824187i	$-0.691633\pi$
$607$	6.35320	−	6.35320i	0.257868	−	0.257868i	0.824187	+	0.566318i	$0.191633\pi$
$608$	−13.3293	−	18.4196i	−0.540575	−	0.747011i
$609$	62.1095			2.51680
$610$	−34.2151	−	24.7757i	−1.38533	−	1.00314i
$611$	9.86965	+	17.1001i	0.399283	+	0.691796i
$612$	0.362487	+	3.86600i	0.0146527	+	0.156274i
$613$	31.3456	+	31.3456i	1.26604	+	1.26604i	0.948118	+	0.317920i	$0.102984\pi$
$613$	31.3456	+	31.3456i	1.26604	+	1.26604i	0.317920	+	0.948118i	$0.397016\pi$
$614$	−4.51653	+	12.5302i	−0.182272	+	0.505679i
$615$	−6.81936	+	23.6461i	−0.274983	+	0.953503i
$616$	−24.6527	−	41.7939i	−0.993287	−	1.68392i
$617$	−9.25716	+	9.25716i	−0.372679	+	0.372679i	−0.868452	−	0.495773i	$-0.834885\pi$
$617$	−9.25716	+	9.25716i	−0.372679	+	0.372679i	0.495773	+	0.868452i	$0.334885\pi$
$618$	−13.2495	+	6.22861i	−0.532974	+	0.250552i
$619$		−	45.3844i		−	1.82415i	−0.410019	−	0.912077i	$-0.634478\pi$
$619$		−	45.3844i		−	1.82415i	0.410019	−	0.912077i	$-0.365522\pi$
$620$	1.96208	−	10.3537i	0.0787991	−	0.415814i
$621$	−13.7596			−0.552152
$622$	−23.5078	+	11.0510i	−0.942577	+	0.443107i
$623$	−19.1072	−	19.1072i	−0.765512	−	0.765512i
$624$	−24.0052	+	20.6516i	−0.960976	+	0.826724i
$625$	−10.8223	−	22.5361i	−0.432893	−	0.901445i
$626$	2.36495	+	0.852448i	0.0945225	+	0.0340707i
$627$	−24.9867	+	24.9867i	−0.997874	+	0.997874i
$628$	−15.0773	+	1.41369i	−0.601649	+	0.0564122i
$629$	−0.685325			−0.0273257
$630$	−24.3597	+	3.89791i	−0.970514	+	0.155296i
$631$	−6.06716			−0.241530			−0.120765	−	0.992681i	$-0.538535\pi$
$631$	−6.06716			−0.241530			−0.120765	+	0.992681i	$0.538535\pi$
$632$	9.42063	+	2.43023i	0.374732	+	0.0966695i
$633$	−32.1377	+	32.1377i	−1.27736	+	1.27736i
$634$	0.573418	+	0.206689i	0.0227733	+	0.00820866i
$635$	1.57403	−	5.45794i	0.0624634	−	0.216592i
$636$	5.33740	−	6.44186i	0.211642	−	0.255436i
$637$	−10.6027	+	39.5482i	−0.420094	+	1.56696i
$638$	−33.8359	+	15.9063i	−1.33958	+	0.629737i
$639$		−	26.7371i		−	1.05771i
$640$	10.7558	+	22.8979i	0.425159	+	0.905119i
$641$	−3.06840			−0.121195			−0.0605973	−	0.998162i	$-0.519301\pi$
$641$	−3.06840			−0.121195			−0.0605973	+	0.998162i	$0.519301\pi$
$642$	14.5518	+	30.9546i	0.574314	+	1.22168i
$643$	−10.4791	+	10.4791i	−0.413254	+	0.413254i	−0.882870	−	0.469617i	$-0.844392\pi$
$643$	−10.4791	+	10.4791i	−0.413254	+	0.413254i	0.469617	+	0.882870i	$0.344392\pi$
$644$	−35.0670	−	29.0548i	−1.38183	−	1.14492i
$645$	14.5248	+	26.2978i	0.571915	+	1.03547i
$646$	−5.70164	−	2.05516i	−0.224328	−	0.0808592i
$647$	−23.5375	+	23.5375i	−0.925356	+	0.925356i	−0.997401	−	0.0720455i	$-0.977047\pi$
$647$	−23.5375	+	23.5375i	−0.925356	+	0.925356i	0.0720455	+	0.997401i	$0.477047\pi$
$648$	30.5292	+	7.87559i	1.19930	+	0.309382i
$649$			3.35552i			0.131716i
$650$	−23.6380	−	9.55223i	−0.927158	−	0.374669i
$651$		−	22.1662i		−	0.868764i
$652$	1.95370	+	20.8367i	0.0765129	+	0.816027i
$653$	−20.8321	+	20.8321i	−0.815224	+	0.815224i	−0.985412	−	0.170187i	$-0.945563\pi$
$653$	−20.8321	+	20.8321i	−0.815224	+	0.815224i	0.170187	+	0.985412i	$0.445563\pi$
$654$	3.33525	−	9.25300i	0.130419	−	0.361821i
$655$	−1.27183	−	2.30269i	−0.0496944	−	0.0899737i
$656$	19.7009	−	3.72718i	0.769189	−	0.145522i
$657$	9.72250	−	9.72250i	0.379311	−	0.379311i
$658$	30.0269	−	14.1157i	1.17057	−	0.550286i
$659$	−15.2442			−0.593831			−0.296916	−	0.954904i	$-0.595958\pi$
$659$	−15.2442			−0.593831			−0.296916	+	0.954904i	$0.595958\pi$
$660$	32.4923	−	22.1393i	1.26476	−	0.861770i
$661$		−	11.3087i		−	0.439857i	−0.975516	−	0.219929i	$-0.929418\pi$
$661$		−	11.3087i		−	0.439857i	0.975516	−	0.219929i	$-0.0705825\pi$
$662$	0.930583	+	1.97954i	0.0361681	+	0.0769369i
$663$	−2.18580	+	8.15307i	−0.0848894	+	0.316639i
$664$	15.4148	−	9.09265i	0.598211	−	0.352863i
$665$	10.6699	−	36.9978i	0.413761	−	1.43471i
$666$	0.561235	−	1.55704i	0.0217474	−	0.0603340i
$667$	−24.8121	+	24.8121i	−0.960728	+	0.960728i
$668$	−13.5945	+	1.27465i	−0.525985	+	0.0493178i
$669$	18.3680			0.710149
$670$	−2.61201	−	16.3236i	−0.100911	−	0.630634i
$671$	53.4901			2.06496
$672$	31.1967	+	43.1103i	1.20344	+	1.66302i
$673$	3.84495	−	3.84495i	0.148212	−	0.148212i	−0.629107	−	0.777319i	$-0.716579\pi$
$673$	3.84495	−	3.84495i	0.148212	−	0.148212i	0.777319	+	0.629107i	$0.216579\pi$
$674$	14.4919	−	40.2051i	0.558209	−	1.54864i
$675$	2.87360	+	12.6221i	0.110605	+	0.485823i
$676$	−24.3787	+	9.03775i	−0.937641	+	0.347606i
$677$	−23.8676	−	23.8676i	−0.917305	−	0.917305i	0.0795281	−	0.996833i	$-0.474659\pi$
$677$	−23.8676	−	23.8676i	−0.917305	−	0.917305i	−0.996833	+	0.0795281i	$0.974659\pi$
$678$	18.2308	+	38.7807i	0.700151	+	1.48936i
$679$	−58.4466			−2.24297
$680$	5.80733	+	3.42793i	0.222701	+	0.131455i
$681$			1.79810i			0.0689033i
$682$	5.67681	+	12.0757i	0.217376	+	0.462403i
$683$	−8.50618	+	8.50618i	−0.325480	+	0.325480i	−0.850865	−	0.525385i	$-0.823921\pi$
$683$	−8.50618	+	8.50618i	−0.325480	+	0.325480i	0.525385	+	0.850865i	$0.323921\pi$
$684$	9.33852	−	11.2709i	0.357067	−	0.430954i
$685$	0.229922	−	0.797254i	0.00878488	−	0.0304615i
$686$	24.8298	+	8.94991i	0.948006	+	0.341709i
$687$	8.77133	+	8.77133i	0.334647	+	0.334647i
$688$	13.7885	−	20.2231i	0.525681	−	0.770997i
$689$	5.94906	−	3.43361i	0.226641	−	0.130810i
$690$	21.6421	−	29.8876i	0.823902	−	1.13780i
$691$	−30.9634			−1.17790			−0.588952	−	0.808168i	$-0.700459\pi$
$691$	−30.9634			−1.17790			−0.588952	+	0.808168i	$0.700459\pi$
$692$	−2.89667	−	30.8936i	−0.110115	−	1.17440i
$693$	22.0882	−	22.0882i	0.839062	−	0.839062i
$694$	−29.8272	−	10.7512i	−1.13222	−	0.408111i
$695$	−12.7001	+	7.01451i	−0.481740	+	0.266076i
$696$	35.3165	−	20.8319i	1.33867	−	0.789633i
$697$	3.77926	−	3.77926i	0.143150	−	0.143150i
$698$	−3.52432	−	7.49693i	−0.133397	−	0.283763i
$699$	16.9135			0.639727
$700$	−19.3293	+	38.2359i	−0.730578	+	1.44518i
$701$	−15.6776			−0.592134			−0.296067	−	0.955167i	$-0.595675\pi$
$701$	−15.6776			−0.592134			−0.296067	+	0.955167i	$0.595675\pi$
$702$	10.8364	+	7.53980i	0.408995	+	0.284571i
$703$	1.82671	+	1.82671i	0.0688958	+	0.0688958i
$704$	−28.0359	−	15.4961i	−1.05664	−	0.584030i
$705$	12.9983	+	23.5339i	0.489544	+	0.886338i
$706$	7.82904	−	21.7202i	0.294650	−	0.817449i
$707$	31.3281	+	31.3281i	1.17821	+	1.17821i
$708$	−0.343532	−	3.66384i	−0.0129107	−	0.137696i
$709$	4.38017			0.164501			0.0822504	−	0.996612i	$-0.473789\pi$
$709$	4.38017			0.164501			0.0822504	+	0.996612i	$0.473789\pi$
$710$	−37.6098	−	27.2339i	−1.41147	−	1.02207i
$711$			6.26322i			0.234889i
$712$	−17.2733	−	4.45599i	−0.647346	−	0.166995i
$713$	8.85519	+	8.85519i	0.331629	+	0.331629i
$714$	13.3445	+	4.81003i	0.499405	+	0.180011i
$715$	31.3367	−	7.75796i	1.17193	−	0.290131i
$716$	8.83478	−	10.6629i	0.330171	−	0.398493i
$717$	−2.69912	+	2.69912i	−0.100800	+	0.100800i
$718$	13.8377	−	6.50511i	0.516418	−	0.242769i
$719$	42.2331			1.57503			0.787514	−	0.616297i	$-0.211368\pi$
$719$	42.2331			1.57503			0.787514	+	0.616297i	$0.211368\pi$
$720$	−12.5440	+	10.3868i	−0.467486	+	0.387095i
$721$			20.2009i			0.752320i
$722$	−1.71190	−	3.64156i	−0.0637104	−	0.135525i
$723$	−2.97890	+	2.97890i	−0.110787	+	0.110787i
$724$	−13.5342	+	16.3347i	−0.502993	+	0.607076i
$725$	27.9427	+	17.5790i	1.03777	+	0.652868i
$726$	−5.29986	+	14.7034i	−0.196696	+	0.545695i
$727$	30.6068	−	30.6068i	1.13514	−	1.13514i	0.145836	−	0.989309i	$-0.453413\pi$
$727$	30.6068	−	30.6068i	1.13514	−	1.13514i	0.989309	−	0.145836i	$-0.0465871\pi$
$728$	11.6962	+	42.0979i	0.433488	+	1.56025i
$729$			3.24346i			0.120128i
$730$	−3.77303	−	23.5793i	−0.139646	−	0.872708i
$731$		−	6.52451i		−	0.241318i
$732$	−58.4050	+	5.47621i	−2.15871	+	0.202407i
$733$	19.4882	+	19.4882i	0.719813	+	0.719813i	0.968567	−	0.248753i	$-0.0800209\pi$
$733$	19.4882	+	19.4882i	0.719813	+	0.719813i	−0.248753	+	0.968567i	$0.580021\pi$
$734$	12.5936	+	4.53938i	0.464839	+	0.167552i
$735$	−15.4493	+	53.5705i	−0.569857	+	1.97598i
$736$	−29.6849	−	4.75934i	−1.09420	−	0.175431i
$737$	14.8014	+	14.8014i	0.545218	+	0.545218i
$738$	5.49140	+	11.6813i	0.202141	+	0.429995i
$739$			22.6467i			0.833073i	0.909119	+	0.416536i	$0.136756\pi$
$739$			22.6467i			0.833073i	−0.909119	+	0.416536i	$0.863244\pi$
$740$	−1.61854	−	2.37543i	−0.0594989	−	0.0873224i
$741$	27.5580	−	15.9056i	1.01237	−	0.584307i
$742$	−4.91079	−	10.4462i	−0.180281	−	0.383493i
$743$	32.8872	−	32.8872i	1.20651	−	1.20651i	0.234365	−	0.972149i	$-0.424699\pi$
$743$	32.8872	−	32.8872i	1.20651	−	1.20651i	0.972149	−	0.234365i	$-0.0753011\pi$
$744$	−7.43471	−	12.6041i	−0.272570	−	0.462089i
$745$	−45.4681	+	25.1130i	−1.66582	+	0.920069i
$746$	−50.4938	−	18.2005i	−1.84871	−	0.666369i
$747$	8.14679	+	8.14679i	0.298075	+	0.298075i
$748$	−8.50165	+	0.797138i	−0.310851	+	0.0291462i
$749$	47.1949			1.72447
$750$	−31.9366	−	13.6111i	−1.16616	−	0.497007i
$751$		−	42.2764i		−	1.54269i	−0.636420	−	0.771343i	$-0.719585\pi$
$751$		−	42.2764i		−	1.54269i	0.636420	−	0.771343i	$-0.280415\pi$
$752$	12.3393	−	18.0976i	0.449968	−	0.659953i
$753$	43.6000	−	43.6000i	1.58887	−	1.58887i
$754$	33.1371	−	5.94468i	1.20678	−	0.216493i
$755$	12.9565	−	7.15617i	0.471536	−	0.260440i
$756$	14.1540	−	17.0828i	0.514776	−	0.621297i
$757$	27.3850	+	27.3850i	0.995323	+	0.995323i	0.999989	−	0.00466596i	$-0.00148523\pi$
$757$	27.3850	+	27.3850i	0.995323	+	0.995323i	−0.00466596	+	0.999989i	$0.501485\pi$
$758$	8.33442	−	3.91802i	0.302720	−	0.142309i
$759$			46.7247i			1.69600i
$760$	−6.34222	−	24.6163i	−0.230057	−	0.892928i
$761$			10.3952i			0.376826i	0.982090	+	0.188413i	$0.0603344\pi$
$761$			10.3952i			0.376826i	−0.982090	+	0.188413i	$0.939666\pi$
$762$	−3.35585	−	7.13857i	−0.121570	−	0.258603i
$763$	−9.59634	−	9.59634i	−0.347411	−	0.347411i
$764$	31.9694	+	26.4882i	1.15661	+	0.958310i
$765$	−1.20297	+	4.17128i	−0.0434934	+	0.150813i
$766$	−11.9926	−	4.32274i	−0.433310	−	0.156187i
$767$	0.782410	−	2.91841i	0.0282512	−	0.105378i
$768$	32.1985	+	14.0497i	1.16186	+	0.506973i
$769$	−54.0884			−1.95048			−0.975239	−	0.221153i	$-0.929018\pi$
$769$	−54.0884			−1.95048			−0.975239	+	0.221153i	$0.929018\pi$
$770$	−8.57182	−	53.5690i	−0.308907	−	1.93049i
$771$		−	41.6077i		−	1.49846i
$772$	9.96765	−	0.934594i	0.358744	−	0.0336368i
$773$	−17.8837	−	17.8837i	−0.643231	−	0.643231i	0.308117	−	0.951348i	$-0.400301\pi$
$773$	−17.8837	−	17.8837i	−0.643231	−	0.643231i	−0.951348	+	0.308117i	$0.900301\pi$
$774$	14.8235	+	5.34314i	0.532820	+	0.192055i
$775$	6.27377	−	9.97247i	0.225361	−	0.358222i
$776$	−33.2338	+	19.6034i	−1.19302	+	0.703721i
$777$	−4.27536	−	4.27536i	−0.153378	−	0.153378i
$778$	39.9344	−	18.7732i	1.43172	−	0.673053i
$779$	−20.1470			−0.721842
$780$	−33.4219	+	11.6790i	−1.19669	+	0.418175i
$781$	58.7971			2.10393
$782$	−7.25254	+	3.40943i	−0.259350	+	0.121921i
$783$	−12.0872	−	12.0872i	−0.431960	−	0.431960i
$784$	44.6325	−	8.44396i	1.59402	−	0.301570i
$785$	−16.2679	−	4.69153i	−0.580625	−	0.167448i
$786$	−3.43651	−	1.23869i	−0.122576	−	0.0441827i
$787$	−16.5529	−	16.5529i	−0.590048	−	0.590048i	0.347597	−	0.937644i	$-0.386998\pi$
$787$	−16.5529	−	16.5529i	−0.590048	−	0.590048i	−0.937644	+	0.347597i	$0.886998\pi$
$788$	4.63393	+	49.4219i	0.165077	+	1.76058i
$789$			16.2346i			0.577966i
$790$	8.81015	+	6.37958i	0.313451	+	0.226975i
$791$	59.1269			2.10231
$792$	5.15121	−	19.9683i	0.183040	−	0.709543i
$793$	−46.5221	−	12.4723i	−1.65205	−	0.442906i
$794$	−14.9785	−	5.39901i	−0.531567	−	0.191604i
$795$	8.18735	−	4.52205i	0.290376	−	0.160381i
$796$	24.4665	−	29.5292i	0.867191	−	1.04664i
$797$	24.1763	+	24.1763i	0.856370	+	0.856370i	0.990908	−	0.134539i	$-0.0429552\pi$
$797$	24.1763	+	24.1763i	0.856370	+	0.856370i	−0.134539	+	0.990908i	$0.542955\pi$
$798$	−22.7483	−	48.3903i	−0.805283	−	1.71300i
$799$		−	5.83879i		−	0.206561i
$800$	1.83363	+	28.2248i	0.0648285	+	0.997896i
$801$		−	11.4840i		−	0.405768i
$802$	44.6066	−	20.9696i	1.57511	−	0.740462i
$803$	21.3806	+	21.3806i	0.754504	+	0.754504i
$804$	−17.6768	−	14.6461i	−0.623413	−	0.516529i
$805$	−24.6163	−	44.5688i	−0.867611	−	1.57084i
$806$	−2.12160	−	11.8263i	−0.0747301	−	0.416564i
$807$	8.21959	−	8.21959i	0.289343	−	0.289343i
$808$	28.3213	+	7.30603i	0.996341	+	0.257025i
$809$		−	30.2268i		−	1.06272i	−0.847147	−	0.531359i	$-0.821682\pi$
$809$		−	30.2268i		−	1.06272i	0.847147	−	0.531359i	$-0.178318\pi$
$810$	28.5508	+	20.6741i	1.00317	+	0.726415i
$811$	53.8249			1.89005			0.945023	−	0.327003i	$-0.106039\pi$
$811$	53.8249			1.89005			0.945023	+	0.327003i	$0.106039\pi$
$812$	−5.28148	−	56.3282i	−0.185344	−	1.97673i
$813$	−31.4670	−	31.4670i	−1.10360	−	1.10360i
$814$	3.42405	+	1.23420i	0.120013	+	0.0432587i
$815$	−6.48366	+	22.4820i	−0.227113	+	0.787511i
$816$	9.20122	−	1.74077i	0.322107	−	0.0609390i
$817$	−17.3909	+	17.3909i	−0.608431	+	0.608431i
$818$	12.9332	+	27.5116i	0.452199	+	0.961919i
$819$	−24.3612	+	14.0605i	−0.851249	+	0.491315i
$820$	22.0249	+	4.17385i	0.769145	+	0.145757i
$821$			32.6885i			1.14084i	0.821355	+	0.570418i	$0.193219\pi$
$821$			32.6885i			1.14084i	−0.821355	+	0.570418i	$0.806781\pi$
$822$	−0.490197	−	1.04275i	−0.0170976	−	0.0363700i
$823$	23.8035	+	23.8035i	0.829738	+	0.829738i	0.987480	−	0.157743i	$-0.0504217\pi$
$823$	23.8035	+	23.8035i	0.829738	+	0.829738i	−0.157743	+	0.987480i	$0.550422\pi$
$824$	6.77551	+	11.4866i	0.236036	+	0.400154i
$825$	42.8620	−	9.75817i	1.49226	−	0.339736i
$826$	−4.77668	−	1.72176i	−0.166202	−	0.0599076i
$827$	3.46542	+	3.46542i	0.120505	+	0.120505i	0.764787	−	0.644283i	$-0.222844\pi$
$827$	3.46542	+	3.46542i	0.120505	+	0.120505i	−0.644283	+	0.764787i	$0.722844\pi$
$828$	−1.80677	−	19.2696i	−0.0627897	−	0.669666i
$829$		−	5.02884i		−	0.174659i	−0.996179	−	0.0873295i	$-0.972167\pi$
$829$		−	5.02884i		−	0.174659i	0.996179	−	0.0873295i	$-0.0278333\pi$
$830$	19.7578	−	3.16154i	0.685803	−	0.109739i
$831$			49.7547i			1.72597i
$832$	20.7705	+	20.0146i	0.720089	+	0.693882i
$833$	8.56195	−	8.56195i	0.296654	−	0.296654i
$834$	−6.83177	+	18.9534i	−0.236565	+	0.656303i
$835$	−14.6679	−	4.23013i	−0.507605	−	0.146390i
$836$	24.7857	+	20.5362i	0.857230	+	0.710258i
$837$	−4.31379	+	4.31379i	−0.149106	+	0.149106i
$838$	−8.60178	−	18.2977i	−0.297144	−	0.632084i
$839$		−	20.8587i		−	0.720123i	−0.932929	−	0.360061i	$-0.882756\pi$
$839$		−	20.8587i		−	0.720123i	0.932929	−	0.360061i	$-0.117244\pi$
$840$	14.8437	+	57.6136i	0.512158	+	1.98786i
$841$	−14.5926			−0.503195
$842$	−42.7001	+	20.0733i	−1.47154	+	0.691773i
$843$	−23.5877	+	23.5877i	−0.812403	+	0.812403i
$844$	31.8790	+	26.4134i	1.09732	+	0.909186i
$845$	−29.0635	−	0.559457i	−0.999815	−	0.0192459i
$846$	13.2656	+	4.78158i	0.456079	+	0.164394i
$847$	15.2490	+	15.2490i	0.523962	+	0.523962i
$848$	−6.29610	−	4.29280i	−0.216209	−	0.147415i
$849$		−	41.7098i		−	1.43148i
$850$	4.64221	+	5.94093i	0.159227	+	0.203772i
$851$	3.41592			0.117096
$852$	−64.1997	+	6.01954i	−2.19945	+	0.206226i
$853$	29.8918	+	29.8918i	1.02348	+	1.02348i	0.999718	+	0.0237593i	$0.00756354\pi$
$853$	29.8918	+	29.8918i	1.02348	+	1.02348i	0.0237593	+	0.999718i	$0.492436\pi$
$854$	−27.4464	+	76.1446i	−0.939196	+	2.60562i
$855$	14.3249	−	7.91196i	0.489902	−	0.270583i
$856$	26.8359	−	15.8295i	0.917231	−	0.541041i
$857$	−12.2099	−	12.2099i	−0.417081	−	0.417081i	0.467115	−	0.884196i	$-0.345293\pi$
$857$	−12.2099	−	12.2099i	−0.417081	−	0.417081i	−0.884196	+	0.467115i	$0.845293\pi$
$858$	25.6036	−	36.7983i	0.874094	−	1.25627i
$859$	−19.2167			−0.655667			−0.327833	−	0.944736i	$-0.606318\pi$
$859$	−19.2167			−0.655667			−0.327833	+	0.944736i	$0.606318\pi$
$860$	22.6148	−	15.4091i	0.771158	−	0.525445i
$861$	47.1533			1.60698
$862$	−2.16093	−	4.59672i	−0.0736014	−	0.156565i
$863$	−10.8080	+	10.8080i	−0.367908	+	0.367908i	−0.866714	−	0.498806i	$-0.833772\pi$
$863$	−10.8080	+	10.8080i	−0.367908	+	0.367908i	0.498806	+	0.866714i	$0.333772\pi$
$864$	2.31850	−	14.4609i	0.0788771	−	0.491971i
$865$	9.61304	−	33.3332i	0.326853	−	1.13336i
$866$	25.9612	+	9.35771i	0.882196	+	0.317988i
$867$	−24.6283	+	24.6283i	−0.836421	+	0.836421i
$868$	−20.1030	+	1.88491i	−0.682339	+	0.0639779i
$869$	−13.7733			−0.467228
$870$	45.2666	−	7.24332i	1.53468	−	0.245572i
$871$	−9.42202	−	16.3246i	−0.319253	−	0.553136i
$872$	−8.67532	−	2.23797i	−0.293784	−	0.0757871i
$873$	−17.5642	−	17.5642i	−0.594457	−	0.594457i
$874$	28.4192	+	10.2437i	0.961292	+	0.346498i
$875$	−35.7433	+	31.8892i	−1.20834	+	1.07805i
$876$	−25.5340	−	21.1562i	−0.862715	−	0.714803i
$877$	4.13679	−	4.13679i	0.139689	−	0.139689i	−0.633804	−	0.773494i	$-0.718507\pi$
$877$	4.13679	−	4.13679i	0.139689	−	0.139689i	0.773494	+	0.633804i	$0.218507\pi$
$878$	10.2853	+	21.8789i	0.347112	+	0.738378i
$879$			26.4383i			0.891743i
$880$	−22.8415	−	27.5852i	−0.769986	−	0.929897i
$881$	−22.4797			−0.757362			−0.378681	−	0.925527i	$-0.623622\pi$
$881$	−22.4797			−0.757362			−0.378681	+	0.925527i	$0.623622\pi$
$882$	12.4408	+	26.4642i	0.418905	+	0.891094i
$883$	−6.83627	−	6.83627i	−0.230059	−	0.230059i	0.582658	−	0.812717i	$-0.302013\pi$
$883$	−6.83627	−	6.83627i	−0.230059	−	0.230059i	−0.812717	+	0.582658i	$0.802013\pi$
$884$	7.58004	+	1.28904i	0.254944	+	0.0433552i
$885$	1.14006	−	3.95316i	0.0383228	−	0.132884i
$886$	0.724575	−	2.01019i	0.0243426	−	0.0675337i
$887$	33.7719	−	33.7719i	1.13395	−	1.13395i	0.144434	−	0.989514i	$-0.453864\pi$
$887$	33.7719	−	33.7719i	1.13395	−	1.13395i	0.989514	−	0.144434i	$-0.0461362\pi$
$888$	−3.86503	−	0.997059i	−0.129702	−	0.0334591i
$889$	−10.8838			−0.365032
$890$	−16.1540	−	11.6974i	−0.541483	−	0.392097i
$891$	−44.6348			−1.49532
$892$	−1.56193	−	16.6583i	−0.0522971	−	0.557761i
$893$	−15.5631	+	15.5631i	−0.520800	+	0.520800i
$894$	−24.4587	+	67.8560i	−0.818023	+	2.26944i
$895$	13.5522	−	7.48516i	0.453000	−	0.250201i
$896$	36.4447	−	31.9588i	1.21753	−	1.06767i
$897$	10.8949	−	40.6380i	0.363769	−	1.35686i
$898$	4.95189	+	10.5337i	0.165247	+	0.351513i
$899$			15.5578i			0.518881i
$900$	−17.2993	+	5.68175i	−0.576642	+	0.189392i
$901$	−2.03129			−0.0676722
$902$	−25.6882	+	12.0760i	−0.855322	+	0.402088i
$903$	40.7028	−	40.7028i	1.35450	−	1.35450i
$904$	33.6206	−	19.8316i	1.11820	−	0.659588i
$905$	−20.7608	+	11.4667i	−0.690113	+	0.381165i
$906$	6.96974	−	19.3362i	0.231554	−	0.642402i
$907$	−20.3060	+	20.3060i	−0.674250	+	0.674250i	−0.958693	−	0.284443i	$-0.908191\pi$
$907$	−20.3060	+	20.3060i	−0.674250	+	0.674250i	0.284443	+	0.958693i	$0.408191\pi$
$908$	1.63073	−	0.152901i	0.0541176	−	0.00507421i
$909$			18.8292i			0.624524i
$910$	−5.03555	+	48.5894i	−0.166927	+	1.61072i
$911$			25.1696i			0.833905i	0.908928	+	0.416953i	$0.136902\pi$
$911$			25.1696i			0.833905i	−0.908928	+	0.416953i	$0.863098\pi$
$912$	−29.1656	−	19.8856i	−0.965768	−	0.658479i
$913$	−17.9154	+	17.9154i	−0.592914	+	0.592914i
$914$	−24.1875	−	8.71839i	−0.800051	−	0.288379i
$915$	−63.0170	−	18.1736i	−2.08328	−	0.600802i
$916$	7.20900	−	8.70074i	0.238192	−	0.287481i
$917$	−3.56403	+	3.56403i	−0.117695	+	0.117695i
$918$	−1.66090	−	3.53306i	−0.0548178	−	0.116608i
$919$	−16.9111			−0.557845			−0.278923	−	0.960314i	$-0.589977\pi$
$919$	−16.9111			−0.557845			−0.278923	+	0.960314i	$0.589977\pi$
$920$	−28.9460	−	17.0861i	−0.954320	−	0.563313i
$921$			20.6790i			0.681398i
$922$	−18.9788	+	8.92197i	−0.625034	+	0.293829i
$923$	−51.1378	−	13.7098i	−1.68322	−	0.451263i
$924$	−58.0099	−	48.0641i	−1.90839	−	1.58119i
$925$	−0.713394	−	3.13353i	−0.0234563	−	0.103030i
$926$	−35.9425	−	12.9555i	−1.18114	−	0.425744i
$927$	−6.07069	+	6.07069i	−0.199388	+	0.199388i
$928$	−21.8960	−	30.2577i	−0.718771	−	0.993259i
$929$	15.9513			0.523345			0.261672	−	0.965157i	$-0.415726\pi$
$929$	15.9513			0.523345			0.261672	+	0.965157i	$0.415726\pi$
$930$	−2.58507	−	16.1552i	−0.0847678	−	0.529750i
$931$	−45.6433			−1.49590
$932$	−1.43824	−	15.3391i	−0.0471111	−	0.502450i
$933$	−28.5168	+	28.5168i	−0.933598	+	0.933598i
$934$	5.11705	+	1.84444i	0.167435	+	0.0603520i
$935$	−9.17298	−	2.64542i	−0.299989	−	0.0865145i
$936$	−9.13621	+	16.1660i	−0.298626	+	0.528401i
$937$	22.6698	+	22.6698i	0.740588	+	0.740588i	0.972691	−	0.232103i	$-0.0745606\pi$
$937$	22.6698	+	22.6698i	0.740588	+	0.740588i	−0.232103	+	0.972691i	$0.574561\pi$
$938$	−28.6650	+	13.4755i	−0.935947	+	0.439990i
$939$	3.90296			0.127368
$940$	20.2380	−	13.7896i	0.660091	−	0.449766i
$941$			29.4209i			0.959095i	0.877516	+	0.479548i	$0.159199\pi$
$941$			29.4209i			0.959095i	−0.877516	+	0.479548i	$0.840801\pi$
$942$	−21.2771	+	10.0024i	−0.693247	+	0.325896i
$943$	−18.8373	+	18.8373i	−0.613426	+	0.613426i
$944$	−3.29359	+	0.623110i	−0.107197	+	0.0202805i
$945$	21.7116	−	11.9918i	0.706280	−	0.390093i
$946$	−11.7500	+	32.5981i	−0.382025	+	1.05985i
$947$	−11.1580	−	11.1580i	−0.362588	−	0.362588i	0.502177	−	0.864765i	$-0.332533\pi$
$947$	−11.1580	−	11.1580i	−0.362588	−	0.362588i	−0.864765	+	0.502177i	$0.832533\pi$
$948$	15.0389	−	1.41009i	0.488441	−	0.0457975i
$949$	−13.6101	−	23.5807i	−0.441801	−	0.765462i
$950$	3.46168	−	28.2091i	0.112312	−	0.915223i
$951$	0.946330			0.0306869
$952$	3.22755	−	12.5114i	0.104605	−	0.405496i
$953$	22.8350	−	22.8350i	0.739699	−	0.739699i	−0.232820	−	0.972520i	$-0.574795\pi$
$953$	22.8350	−	22.8350i	0.739699	−	0.739699i	0.972520	+	0.232820i	$0.0747954\pi$
$954$	1.66349	−	4.61504i	0.0538575	−	0.149417i
$955$	22.4418	+	40.6318i	0.726201	+	1.31482i
$956$	2.67740	+	2.21836i	0.0865932	+	0.0717468i
$957$	−41.0456	+	41.0456i	−1.32682	+	1.32682i
$958$	17.8108	−	8.37287i	0.575440	−	0.270515i
$959$	−1.58983			−0.0513382
$960$	27.7644	+	27.7814i	0.896093	+	0.896641i
$961$	−25.4476			−0.820890
$962$	−2.69023	−	1.87182i	−0.0867365	−	0.0603497i
$963$	14.1828	+	14.1828i	0.457036	+	0.457036i
$964$	2.95493	+	2.44831i	0.0951719	+	0.0788547i
$965$	10.7547	+	3.10159i	0.346208	+	0.0998438i
$966$	−66.5140	−	23.9750i	−2.14005	−	0.771383i
$967$	−35.4854	−	35.4854i	−1.14113	−	1.14113i	−0.988243	−	0.152890i	$-0.951142\pi$
$967$	−35.4854	−	35.4854i	−1.14113	−	1.14113i	−0.152890	−	0.988243i	$-0.548858\pi$
$968$	13.7855	+	3.55623i	0.443082	+	0.114302i
$969$	−9.40960			−0.302280
$970$	−42.5971	+	6.81615i	−1.36771	+	0.218853i
$971$			28.9193i			0.928065i	0.885818	+	0.464032i	$0.153598\pi$
$971$			28.9193i			0.928065i	−0.885818	+	0.464032i	$0.846402\pi$
$972$	33.2699	−	3.11948i	1.06713	−	0.100057i
$973$	19.6567	+	19.6567i	0.630164	+	0.630164i
$974$	9.55008	−	26.4948i	0.306004	−	0.848949i
$975$	−39.5538	−	1.50717i	−1.26674	−	0.0482680i
$976$	9.93295	+	52.5029i	0.317946	+	1.68058i
$977$	12.4041	−	12.4041i	0.396843	−	0.396843i	−0.480275	−	0.877118i	$-0.659463\pi$
$977$	12.4041	−	12.4041i	0.396843	−	0.396843i	0.877118	+	0.480275i	$0.159463\pi$
$978$	13.8232	+	29.4048i	0.442019	+	0.940263i
$979$	25.2543			0.807131
$980$	49.8977	+	9.45591i	1.59392	+	0.302058i
$981$		−	5.76771i		−	0.184149i
$982$	7.32228	−	3.44221i	0.233663	−	0.109845i
$983$	17.3330	−	17.3330i	0.552836	−	0.552836i	−0.374422	−	0.927258i	$-0.622159\pi$
$983$	17.3330	−	17.3330i	0.552836	−	0.552836i	0.927258	+	0.374422i	$0.122159\pi$
$984$	26.8122	−	15.8156i	0.854742	−	0.504182i
$985$	−15.3784	+	53.3245i	−0.489997	+	1.69906i
$986$	−9.36606	−	3.37600i	−0.298276	−	0.107514i
$987$	36.4249	−	36.4249i	1.15942	−	1.15942i
$988$	−16.7685	−	23.6403i	−0.533476	−	0.752097i
$989$			32.5207i			1.03410i
$990$	13.5224	−	18.6743i	0.429769	−	0.593509i
$991$			56.4299i			1.79255i	0.443495	+	0.896277i	$0.353739\pi$
$991$			56.4299i			1.79255i	−0.443495	+	0.896277i	$0.646261\pi$
$992$	−10.7987	+	7.81446i	−0.342859	+	0.248109i
$993$	2.40133	+	2.40133i	0.0762040	+	0.0762040i
$994$	−30.1695	+	83.6994i	−0.956918	+	2.65478i
$995$	37.5305	−	20.7289i	1.18980	−	0.657151i
$996$	17.7275	−	21.3958i	0.561716	−	0.677950i
$997$	−26.2285	−	26.2285i	−0.830664	−	0.830664i	0.156943	−	0.987608i	$-0.449836\pi$
$997$	−26.2285	−	26.2285i	−0.830664	−	0.830664i	−0.987608	+	0.156943i	$0.949836\pi$
$998$	23.8449	−	11.2095i	0.754797	−	0.354831i
$999$			1.66406i			0.0526486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.p.d.207.12	yes	64
4.3	odd	2	inner	260.2.p.d.207.28	yes	64
5.3	odd	4	inner	260.2.p.d.103.5	✓	64
13.12	even	2	inner	260.2.p.d.207.21	yes	64
20.3	even	4	inner	260.2.p.d.103.21	yes	64
52.51	odd	2	inner	260.2.p.d.207.5	yes	64
65.38	odd	4	inner	260.2.p.d.103.28	yes	64
260.103	even	4	inner	260.2.p.d.103.12	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.p.d.103.5	✓	64	5.3	odd	4	inner
260.2.p.d.103.12	yes	64	260.103	even	4	inner
260.2.p.d.103.21	yes	64	20.3	even	4	inner
260.2.p.d.103.28	yes	64	65.38	odd	4	inner
260.2.p.d.207.5	yes	64	52.51	odd	2	inner
260.2.p.d.207.12	yes	64	1.1	even	1	trivial
260.2.p.d.207.21	yes	64	13.12	even	2	inner
260.2.p.d.207.28	yes	64	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.601658 - 1.27985i) q^{2} +(-1.55255 - 1.55255i) q^{3} +(-1.27602 + 1.54006i) q^{4} +(-1.95736 + 1.08109i) q^{5} +(-1.05293 + 2.92114i) q^{6} +(3.02953 + 3.02953i) q^{7} +(2.73876 + 0.706517i) q^{8} +1.82084i q^{9} +O(q^{10})\)	\(q+(-0.601658 - 1.27985i) q^{2} +(-1.55255 - 1.55255i) q^{3} +(-1.27602 + 1.54006i) q^{4} +(-1.95736 + 1.08109i) q^{5} +(-1.05293 + 2.92114i) q^{6} +(3.02953 + 3.02953i) q^{7} +(2.73876 + 0.706517i) q^{8} +1.82084i q^{9} +(2.56129 + 1.85467i) q^{10} -4.00418 q^{11} +(4.37211 - 0.409941i) q^{12} +(3.48257 + 0.933659i) q^{13} +(2.05459 - 5.70007i) q^{14} +(4.71735 + 1.36045i) q^{15} +(-0.743565 - 3.93028i) q^{16} +(-0.753955 - 0.753955i) q^{17} +(2.33040 - 1.09552i) q^{18} +4.01929i q^{19} +(0.832676 - 4.39393i) q^{20} -9.40700i q^{21} +(2.40915 + 5.12474i) q^{22} +(3.75800 + 3.75800i) q^{23} +(-3.15517 - 5.34898i) q^{24} +(2.66249 - 4.23216i) q^{25} +(-0.900372 - 5.01890i) q^{26} +(-1.83070 + 1.83070i) q^{27} +(-8.53137 + 0.799924i) q^{28} +6.60247i q^{29} +(-1.09706 - 6.85601i) q^{30} +2.35636 q^{31} +(-4.58279 + 3.31633i) q^{32} +(6.21670 + 6.21670i) q^{33} +(-0.511324 + 1.41857i) q^{34} +(-9.20505 - 2.65467i) q^{35} +(-2.80421 - 2.32343i) q^{36} +(0.454487 - 0.454487i) q^{37} +(5.14408 - 2.41824i) q^{38} +(-3.95732 - 6.85643i) q^{39} +(-6.12455 + 1.57795i) q^{40} +5.01258i q^{41} +(-12.0395 + 5.65979i) q^{42} +(4.32686 + 4.32686i) q^{43} +(5.10940 - 6.16667i) q^{44} +(-1.96850 - 3.56404i) q^{45} +(2.54863 - 7.07069i) q^{46} +(3.87211 + 3.87211i) q^{47} +(-4.94755 + 7.25639i) q^{48} +11.3561i q^{49} +(-7.01842 - 0.861267i) q^{50} +2.34111i q^{51} +(-5.88170 + 4.17200i) q^{52} +(1.34709 - 1.34709i) q^{53} +(3.44448 + 1.24156i) q^{54} +(7.83761 - 4.32888i) q^{55} +(6.15675 + 10.4376i) q^{56} +(6.24016 - 6.24016i) q^{57} +(8.45015 - 3.97243i) q^{58} -0.838004i q^{59} +(-8.11459 + 5.52904i) q^{60} -13.3586 q^{61} +(-1.41772 - 3.01578i) q^{62} +(-5.51629 + 5.51629i) q^{63} +(7.00167 + 3.86997i) q^{64} +(-7.82600 + 1.93747i) q^{65} +(4.21610 - 11.6968i) q^{66} +(-3.69649 - 3.69649i) q^{67} +(2.12319 - 0.199076i) q^{68} -11.6690i q^{69} +(2.14072 + 13.3783i) q^{70} -14.6839 q^{71} +(-1.28646 + 4.98686i) q^{72} +(-5.33956 - 5.33956i) q^{73} +(-0.855119 - 0.308228i) q^{74} +(-10.7043 + 2.43700i) q^{75} +(-6.18994 - 5.12868i) q^{76} +(-12.1308 - 12.1308i) q^{77} +(-6.39423 + 9.18998i) q^{78} +3.43974 q^{79} +(5.70441 + 6.88910i) q^{80} +11.1471 q^{81} +(6.41534 - 3.01586i) q^{82} +(4.47418 - 4.47418i) q^{83} +(14.4873 + 12.0035i) q^{84} +(2.29085 + 0.660665i) q^{85} +(2.93443 - 8.14100i) q^{86} +(10.2507 - 10.2507i) q^{87} +(-10.9665 - 2.82902i) q^{88} -6.30698 q^{89} +(-3.37706 + 4.66371i) q^{90} +(7.72198 + 13.3791i) q^{91} +(-10.5828 + 0.992272i) q^{92} +(-3.65837 - 3.65837i) q^{93} +(2.62602 - 7.28539i) q^{94} +(-4.34522 - 7.86718i) q^{95} +(12.2638 + 1.96624i) q^{96} +(-9.64616 + 9.64616i) q^{97} +(14.5340 - 6.83245i) q^{98} -7.29099i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q+O(q^{10}) \) 64 * q	\( 64 q - 24 q^{12} - 4 q^{16} - 40 q^{17} - 36 q^{22} + 44 q^{26} + 24 q^{30} + 28 q^{36} + 16 q^{38} - 44 q^{40} + 8 q^{42} - 44 q^{48} + 56 q^{52} - 48 q^{53} - 64 q^{56} + 80 q^{61} + 20 q^{62} - 72 q^{65} - 24 q^{66} - 76 q^{68} - 112 q^{77} - 20 q^{78} + 80 q^{81} + 52 q^{82} - 152 q^{88} - 64 q^{90} + 56 q^{92}+O(q^{100}) \) 64 * q - 24 * q^12 - 4 * q^16 - 40 * q^17 - 36 * q^22 + 44 * q^26 + 24 * q^30 + 28 * q^36 + 16 * q^38 - 44 * q^40 + 8 * q^42 - 44 * q^48 + 56 * q^52 - 48 * q^53 - 64 * q^56 + 80 * q^61 + 20 * q^62 - 72 * q^65 - 24 * q^66 - 76 * q^68 - 112 * q^77 - 20 * q^78 + 80 * q^81 + 52 * q^82 - 152 * q^88 - 64 * q^90 + 56 * q^92

Introduction

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